/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 17 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 15 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) AND (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 36 ms] (13) YES (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 368 ms] (16) YES (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] (25) YES (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy _ [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = (\(ys,_) ->ys) vv10; zs = (\(_,zs) ->zs) vv10; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\(_,zs)->zs" is transformed to "zs0 (_,zs) = zs; " The following Lambda expression "\(ys,_)->ys" is transformed to "ys0 (ys,_) = ys; " The following Lambda expression "\(_,zs)->zs" is transformed to "zs1 (_,zs) = zs; " The following Lambda expression "\(ys,_)->ys" is transformed to "ys1 (ys,_) = ys; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy _ [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,_) = ys; zs = zs1 vv10; zs1 (_,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. Binding Reductions: The bind variable of the following binding Pattern "xs@(vz : wu)" is replaced by the following term "vz : wu" ---------------------------------------- (4) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,yv) = ys; zs = zs1 vv10; zs1 (yw,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "span p [] = ([],[]); span p (vz : wu)|p vz(vz : ys,zs)|otherwise([],vz : wu) where { vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,zs) = zs; } ; " is transformed to "span p [] = span3 p []; span p (vz : wu) = span2 p (vz : wu); " "span2 p (vz : wu) = span1 p vz wu (p vz) where { span0 p vz wu True = ([],vz : wu); ; span1 p vz wu True = (vz : ys,zs); span1 p vz wu False = span0 p vz wu otherwise; ; vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,zs) = zs; } ; " "span3 p [] = ([],[]); span3 yz zu = span2 yz zu; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,yv) = ys; zs = zs1 vv10; zs1 (yw,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "span1 p vz wu (p vz) where { span0 p vz wu True = ([],vz : wu); ; span1 p vz wu True = (vz : ys,zs); span1 p vz wu False = span0 p vz wu otherwise; ; vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,zs) = zs; } " are unpacked to the following functions on top level "span2Span0 zv zw p vz wu True = ([],vz : wu); " "span2Zs zv zw = span2Zs0 zv zw (span2Vu43 zv zw); " "span2Zs0 zv zw (wv,zs) = zs; " "span2Ys zv zw = span2Ys0 zv zw (span2Vu43 zv zw); " "span2Ys0 zv zw (ys,ww) = ys; " "span2Vu43 zv zw = span zv zw; " "span2Span1 zv zw p vz wu True = (vz : span2Ys zv zw,span2Zs zv zw); span2Span1 zv zw p vz wu False = span2Span0 zv zw p vz wu otherwise; " The bindings of the following Let/Where expression "(x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ; ys = ys1 vv10; ; ys1 (ys,yv) = ys; ; zs = zs1 vv10; ; zs1 (yw,zs) = zs; } " are unpacked to the following functions on top level "groupByZs zx zy zz = groupByZs1 zx zy zz (groupByVv10 zx zy zz); " "groupByYs1 zx zy zz (ys,yv) = ys; " "groupByYs zx zy zz = groupByYs1 zx zy zz (groupByVv10 zx zy zz); " "groupByVv10 zx zy zz = span (zx zy) zz; " "groupByZs1 zx zy zz (yw,zs) = zs; " ---------------------------------------- (8) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : groupByYs eq x xs) : groupBy eq (groupByZs eq x xs); groupByVv10 zx zy zz = span (zx zy) zz; groupByYs zx zy zz = groupByYs1 zx zy zz (groupByVv10 zx zy zz); groupByYs1 zx zy zz (ys,yv) = ys; groupByZs zx zy zz = groupByZs1 zx zy zz (groupByVv10 zx zy zz); groupByZs1 zx zy zz (yw,zs) = zs; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.group",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.group vuu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="List.groupBy (==) vuu3",fontsize=16,color="burlywood",shape="triangle"];859[label="vuu3/vuu30 : vuu31",fontsize=10,color="white",style="solid",shape="box"];4 -> 859[label="",style="solid", color="burlywood", weight=9]; 859 -> 5[label="",style="solid", color="burlywood", weight=3]; 860[label="vuu3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 860[label="",style="solid", color="burlywood", weight=9]; 860 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="List.groupBy (==) (vuu30 : vuu31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="List.groupBy (==) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="(vuu30 : List.groupByYs (==) vuu30 vuu31) : List.groupBy (==) (List.groupByZs (==) vuu30 vuu31)",fontsize=16,color="green",shape="box"];7 -> 9[label="",style="dashed", color="green", weight=3]; 7 -> 10[label="",style="dashed", color="green", weight=3]; 8[label="[]",fontsize=16,color="green",shape="box"];9[label="List.groupByYs (==) vuu30 vuu31",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10 -> 4[label="",style="dashed", color="red", weight=0]; 10[label="List.groupBy (==) (List.groupByZs (==) vuu30 vuu31)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3]; 11[label="List.groupByYs1 (==) vuu30 vuu31 (List.groupByVv10 (==) vuu30 vuu31)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="List.groupByZs (==) vuu30 vuu31",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="List.groupByYs1 (==) vuu30 vuu31 (span ((==) vuu30) vuu31)",fontsize=16,color="burlywood",shape="box"];861[label="vuu31/vuu310 : vuu311",fontsize=10,color="white",style="solid",shape="box"];13 -> 861[label="",style="solid", color="burlywood", weight=9]; 861 -> 15[label="",style="solid", color="burlywood", weight=3]; 862[label="vuu31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 862[label="",style="solid", color="burlywood", weight=9]; 862 -> 16[label="",style="solid", color="burlywood", weight=3]; 14[label="List.groupByZs1 (==) vuu30 vuu31 (List.groupByVv10 (==) vuu30 vuu31)",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3]; 15[label="List.groupByYs1 (==) vuu30 (vuu310 : vuu311) (span ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3]; 16[label="List.groupByYs1 (==) vuu30 [] (span ((==) vuu30) [])",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3]; 17[label="List.groupByZs1 (==) vuu30 vuu31 (span ((==) vuu30) vuu31)",fontsize=16,color="burlywood",shape="box"];863[label="vuu31/vuu310 : vuu311",fontsize=10,color="white",style="solid",shape="box"];17 -> 863[label="",style="solid", color="burlywood", weight=9]; 863 -> 20[label="",style="solid", color="burlywood", weight=3]; 864[label="vuu31/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 864[label="",style="solid", color="burlywood", weight=9]; 864 -> 21[label="",style="solid", color="burlywood", weight=3]; 18[label="List.groupByYs1 (==) vuu30 (vuu310 : vuu311) (span2 ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="List.groupByYs1 (==) vuu30 [] (span3 ((==) vuu30) [])",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="List.groupByZs1 (==) vuu30 [] (span ((==) vuu30) [])",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22 -> 26[label="",style="dashed", color="red", weight=0]; 22[label="List.groupByYs1 (==) vuu30 (vuu310 : vuu311) (span2Span1 ((==) vuu30) vuu311 ((==) vuu30) vuu310 vuu311 ((==) vuu30 vuu310))",fontsize=16,color="magenta"];22 -> 27[label="",style="dashed", color="magenta", weight=3]; 22 -> 28[label="",style="dashed", color="magenta", weight=3]; 22 -> 29[label="",style="dashed", color="magenta", weight=3]; 22 -> 30[label="",style="dashed", color="magenta", weight=3]; 23[label="List.groupByYs1 (==) vuu30 [] ([],[])",fontsize=16,color="black",shape="box"];23 -> 31[label="",style="solid", color="black", weight=3]; 24[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span2 ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];24 -> 32[label="",style="solid", color="black", weight=3]; 25[label="List.groupByZs1 (==) vuu30 [] (span3 ((==) vuu30) [])",fontsize=16,color="black",shape="box"];25 -> 33[label="",style="solid", color="black", weight=3]; 27[label="vuu310",fontsize=16,color="green",shape="box"];28[label="vuu30",fontsize=16,color="green",shape="box"];29[label="vuu311",fontsize=16,color="green",shape="box"];30[label="(==) vuu30 vuu310",fontsize=16,color="blue",shape="box"];865[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 865[label="",style="solid", color="blue", weight=9]; 865 -> 34[label="",style="solid", color="blue", weight=3]; 866[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 866[label="",style="solid", color="blue", weight=9]; 866 -> 35[label="",style="solid", color="blue", weight=3]; 867[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 867[label="",style="solid", color="blue", weight=9]; 867 -> 36[label="",style="solid", color="blue", weight=3]; 868[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 868[label="",style="solid", color="blue", weight=9]; 868 -> 37[label="",style="solid", color="blue", weight=3]; 869[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 869[label="",style="solid", color="blue", weight=9]; 869 -> 38[label="",style="solid", color="blue", weight=3]; 870[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 870[label="",style="solid", color="blue", weight=9]; 870 -> 39[label="",style="solid", color="blue", weight=3]; 871[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 871[label="",style="solid", color="blue", weight=9]; 871 -> 40[label="",style="solid", color="blue", weight=3]; 872[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 872[label="",style="solid", color="blue", weight=9]; 872 -> 41[label="",style="solid", color="blue", weight=3]; 873[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 873[label="",style="solid", color="blue", weight=9]; 873 -> 42[label="",style="solid", color="blue", weight=3]; 874[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 874[label="",style="solid", color="blue", weight=9]; 874 -> 43[label="",style="solid", color="blue", weight=3]; 875[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 875[label="",style="solid", color="blue", weight=9]; 875 -> 44[label="",style="solid", color="blue", weight=3]; 876[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 876[label="",style="solid", color="blue", weight=9]; 876 -> 45[label="",style="solid", color="blue", weight=3]; 877[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 877[label="",style="solid", color="blue", weight=9]; 877 -> 46[label="",style="solid", color="blue", weight=3]; 878[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 878[label="",style="solid", color="blue", weight=9]; 878 -> 47[label="",style="solid", color="blue", weight=3]; 26[label="List.groupByYs1 (==) vuu9 (vuu10 : vuu11) (span2Span1 ((==) vuu9) vuu11 ((==) vuu9) vuu10 vuu11 vuu12)",fontsize=16,color="burlywood",shape="triangle"];879[label="vuu12/False",fontsize=10,color="white",style="solid",shape="box"];26 -> 879[label="",style="solid", color="burlywood", weight=9]; 879 -> 48[label="",style="solid", color="burlywood", weight=3]; 880[label="vuu12/True",fontsize=10,color="white",style="solid",shape="box"];26 -> 880[label="",style="solid", color="burlywood", weight=9]; 880 -> 49[label="",style="solid", color="burlywood", weight=3]; 31[label="[]",fontsize=16,color="green",shape="box"];32 -> 50[label="",style="dashed", color="red", weight=0]; 32[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span2Span1 ((==) vuu30) vuu311 ((==) vuu30) vuu310 vuu311 ((==) vuu30 vuu310))",fontsize=16,color="magenta"];32 -> 51[label="",style="dashed", color="magenta", weight=3]; 32 -> 52[label="",style="dashed", color="magenta", weight=3]; 32 -> 53[label="",style="dashed", color="magenta", weight=3]; 32 -> 54[label="",style="dashed", color="magenta", weight=3]; 33[label="List.groupByZs1 (==) vuu30 [] ([],[])",fontsize=16,color="black",shape="box"];33 -> 55[label="",style="solid", color="black", weight=3]; 34[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];881[label="vuu30/()",fontsize=10,color="white",style="solid",shape="box"];34 -> 881[label="",style="solid", color="burlywood", weight=9]; 881 -> 56[label="",style="solid", color="burlywood", weight=3]; 35[label="(==) vuu30 vuu310",fontsize=16,color="black",shape="triangle"];35 -> 57[label="",style="solid", color="black", weight=3]; 36[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];882[label="vuu30/vuu300 : vuu301",fontsize=10,color="white",style="solid",shape="box"];36 -> 882[label="",style="solid", color="burlywood", weight=9]; 882 -> 58[label="",style="solid", color="burlywood", weight=3]; 883[label="vuu30/[]",fontsize=10,color="white",style="solid",shape="box"];36 -> 883[label="",style="solid", color="burlywood", weight=9]; 883 -> 59[label="",style="solid", color="burlywood", weight=3]; 37[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];884[label="vuu30/Integer vuu300",fontsize=10,color="white",style="solid",shape="box"];37 -> 884[label="",style="solid", color="burlywood", weight=9]; 884 -> 60[label="",style="solid", color="burlywood", weight=3]; 38[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];885[label="vuu30/(vuu300,vuu301,vuu302)",fontsize=10,color="white",style="solid",shape="box"];38 -> 885[label="",style="solid", color="burlywood", weight=9]; 885 -> 61[label="",style="solid", color="burlywood", weight=3]; 39[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];886[label="vuu30/LT",fontsize=10,color="white",style="solid",shape="box"];39 -> 886[label="",style="solid", color="burlywood", weight=9]; 886 -> 62[label="",style="solid", color="burlywood", weight=3]; 887[label="vuu30/EQ",fontsize=10,color="white",style="solid",shape="box"];39 -> 887[label="",style="solid", color="burlywood", weight=9]; 887 -> 63[label="",style="solid", color="burlywood", weight=3]; 888[label="vuu30/GT",fontsize=10,color="white",style="solid",shape="box"];39 -> 888[label="",style="solid", color="burlywood", weight=9]; 888 -> 64[label="",style="solid", color="burlywood", weight=3]; 40[label="(==) vuu30 vuu310",fontsize=16,color="black",shape="triangle"];40 -> 65[label="",style="solid", color="black", weight=3]; 41[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];889[label="vuu30/vuu300 :% vuu301",fontsize=10,color="white",style="solid",shape="box"];41 -> 889[label="",style="solid", color="burlywood", weight=9]; 889 -> 66[label="",style="solid", color="burlywood", weight=3]; 42[label="(==) vuu30 vuu310",fontsize=16,color="black",shape="triangle"];42 -> 67[label="",style="solid", color="black", weight=3]; 43[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];890[label="vuu30/Left vuu300",fontsize=10,color="white",style="solid",shape="box"];43 -> 890[label="",style="solid", color="burlywood", weight=9]; 890 -> 68[label="",style="solid", color="burlywood", weight=3]; 891[label="vuu30/Right vuu300",fontsize=10,color="white",style="solid",shape="box"];43 -> 891[label="",style="solid", color="burlywood", weight=9]; 891 -> 69[label="",style="solid", color="burlywood", weight=3]; 44[label="(==) vuu30 vuu310",fontsize=16,color="black",shape="triangle"];44 -> 70[label="",style="solid", color="black", weight=3]; 45[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];892[label="vuu30/False",fontsize=10,color="white",style="solid",shape="box"];45 -> 892[label="",style="solid", color="burlywood", weight=9]; 892 -> 71[label="",style="solid", color="burlywood", weight=3]; 893[label="vuu30/True",fontsize=10,color="white",style="solid",shape="box"];45 -> 893[label="",style="solid", color="burlywood", weight=9]; 893 -> 72[label="",style="solid", color="burlywood", weight=3]; 46[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];894[label="vuu30/(vuu300,vuu301)",fontsize=10,color="white",style="solid",shape="box"];46 -> 894[label="",style="solid", color="burlywood", weight=9]; 894 -> 73[label="",style="solid", color="burlywood", weight=3]; 47[label="(==) vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];895[label="vuu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];47 -> 895[label="",style="solid", color="burlywood", weight=9]; 895 -> 74[label="",style="solid", color="burlywood", weight=3]; 896[label="vuu30/Just vuu300",fontsize=10,color="white",style="solid",shape="box"];47 -> 896[label="",style="solid", color="burlywood", weight=9]; 896 -> 75[label="",style="solid", color="burlywood", weight=3]; 48[label="List.groupByYs1 (==) vuu9 (vuu10 : vuu11) (span2Span1 ((==) vuu9) vuu11 ((==) vuu9) vuu10 vuu11 False)",fontsize=16,color="black",shape="box"];48 -> 76[label="",style="solid", color="black", weight=3]; 49[label="List.groupByYs1 (==) vuu9 (vuu10 : vuu11) (span2Span1 ((==) vuu9) vuu11 ((==) vuu9) vuu10 vuu11 True)",fontsize=16,color="black",shape="box"];49 -> 77[label="",style="solid", color="black", weight=3]; 51[label="vuu310",fontsize=16,color="green",shape="box"];52[label="vuu30",fontsize=16,color="green",shape="box"];53[label="(==) vuu30 vuu310",fontsize=16,color="blue",shape="box"];897[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 897[label="",style="solid", color="blue", weight=9]; 897 -> 78[label="",style="solid", color="blue", weight=3]; 898[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 898[label="",style="solid", color="blue", weight=9]; 898 -> 79[label="",style="solid", color="blue", weight=3]; 899[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 899[label="",style="solid", color="blue", weight=9]; 899 -> 80[label="",style="solid", color="blue", weight=3]; 900[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 900[label="",style="solid", color="blue", weight=9]; 900 -> 81[label="",style="solid", color="blue", weight=3]; 901[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 901[label="",style="solid", color="blue", weight=9]; 901 -> 82[label="",style="solid", color="blue", weight=3]; 902[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 902[label="",style="solid", color="blue", weight=9]; 902 -> 83[label="",style="solid", color="blue", weight=3]; 903[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 903[label="",style="solid", color="blue", weight=9]; 903 -> 84[label="",style="solid", color="blue", weight=3]; 904[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 904[label="",style="solid", color="blue", weight=9]; 904 -> 85[label="",style="solid", color="blue", weight=3]; 905[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 905[label="",style="solid", color="blue", weight=9]; 905 -> 86[label="",style="solid", color="blue", weight=3]; 906[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 906[label="",style="solid", color="blue", weight=9]; 906 -> 87[label="",style="solid", color="blue", weight=3]; 907[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 907[label="",style="solid", color="blue", weight=9]; 907 -> 88[label="",style="solid", color="blue", weight=3]; 908[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 908[label="",style="solid", color="blue", weight=9]; 908 -> 89[label="",style="solid", color="blue", weight=3]; 909[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 909[label="",style="solid", color="blue", weight=9]; 909 -> 90[label="",style="solid", color="blue", weight=3]; 910[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];53 -> 910[label="",style="solid", color="blue", weight=9]; 910 -> 91[label="",style="solid", color="blue", weight=3]; 54[label="vuu311",fontsize=16,color="green",shape="box"];50[label="List.groupByZs1 (==) vuu18 (vuu19 : vuu20) (span2Span1 ((==) vuu18) vuu20 ((==) vuu18) vuu19 vuu20 vuu21)",fontsize=16,color="burlywood",shape="triangle"];911[label="vuu21/False",fontsize=10,color="white",style="solid",shape="box"];50 -> 911[label="",style="solid", color="burlywood", weight=9]; 911 -> 92[label="",style="solid", color="burlywood", weight=3]; 912[label="vuu21/True",fontsize=10,color="white",style="solid",shape="box"];50 -> 912[label="",style="solid", color="burlywood", weight=9]; 912 -> 93[label="",style="solid", color="burlywood", weight=3]; 55[label="[]",fontsize=16,color="green",shape="box"];56[label="(==) () vuu310",fontsize=16,color="burlywood",shape="box"];913[label="vuu310/()",fontsize=10,color="white",style="solid",shape="box"];56 -> 913[label="",style="solid", color="burlywood", weight=9]; 913 -> 94[label="",style="solid", color="burlywood", weight=3]; 57[label="primEqFloat vuu30 vuu310",fontsize=16,color="burlywood",shape="box"];914[label="vuu30/Float vuu300 vuu301",fontsize=10,color="white",style="solid",shape="box"];57 -> 914[label="",style="solid", color="burlywood", weight=9]; 914 -> 95[label="",style="solid", color="burlywood", weight=3]; 58[label="(==) vuu300 : vuu301 vuu310",fontsize=16,color="burlywood",shape="box"];915[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];58 -> 915[label="",style="solid", color="burlywood", weight=9]; 915 -> 96[label="",style="solid", color="burlywood", weight=3]; 916[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];58 -> 916[label="",style="solid", color="burlywood", weight=9]; 916 -> 97[label="",style="solid", color="burlywood", weight=3]; 59[label="(==) [] vuu310",fontsize=16,color="burlywood",shape="box"];917[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];59 -> 917[label="",style="solid", color="burlywood", weight=9]; 917 -> 98[label="",style="solid", color="burlywood", weight=3]; 918[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];59 -> 918[label="",style="solid", color="burlywood", weight=9]; 918 -> 99[label="",style="solid", color="burlywood", weight=3]; 60[label="(==) Integer vuu300 vuu310",fontsize=16,color="burlywood",shape="box"];919[label="vuu310/Integer vuu3100",fontsize=10,color="white",style="solid",shape="box"];60 -> 919[label="",style="solid", color="burlywood", weight=9]; 919 -> 100[label="",style="solid", color="burlywood", weight=3]; 61[label="(==) (vuu300,vuu301,vuu302) vuu310",fontsize=16,color="burlywood",shape="box"];920[label="vuu310/(vuu3100,vuu3101,vuu3102)",fontsize=10,color="white",style="solid",shape="box"];61 -> 920[label="",style="solid", color="burlywood", weight=9]; 920 -> 101[label="",style="solid", color="burlywood", weight=3]; 62[label="(==) LT vuu310",fontsize=16,color="burlywood",shape="box"];921[label="vuu310/LT",fontsize=10,color="white",style="solid",shape="box"];62 -> 921[label="",style="solid", color="burlywood", weight=9]; 921 -> 102[label="",style="solid", color="burlywood", weight=3]; 922[label="vuu310/EQ",fontsize=10,color="white",style="solid",shape="box"];62 -> 922[label="",style="solid", color="burlywood", weight=9]; 922 -> 103[label="",style="solid", color="burlywood", weight=3]; 923[label="vuu310/GT",fontsize=10,color="white",style="solid",shape="box"];62 -> 923[label="",style="solid", color="burlywood", weight=9]; 923 -> 104[label="",style="solid", color="burlywood", weight=3]; 63[label="(==) EQ vuu310",fontsize=16,color="burlywood",shape="box"];924[label="vuu310/LT",fontsize=10,color="white",style="solid",shape="box"];63 -> 924[label="",style="solid", color="burlywood", weight=9]; 924 -> 105[label="",style="solid", color="burlywood", weight=3]; 925[label="vuu310/EQ",fontsize=10,color="white",style="solid",shape="box"];63 -> 925[label="",style="solid", color="burlywood", weight=9]; 925 -> 106[label="",style="solid", color="burlywood", weight=3]; 926[label="vuu310/GT",fontsize=10,color="white",style="solid",shape="box"];63 -> 926[label="",style="solid", color="burlywood", weight=9]; 926 -> 107[label="",style="solid", color="burlywood", weight=3]; 64[label="(==) GT vuu310",fontsize=16,color="burlywood",shape="box"];927[label="vuu310/LT",fontsize=10,color="white",style="solid",shape="box"];64 -> 927[label="",style="solid", color="burlywood", weight=9]; 927 -> 108[label="",style="solid", color="burlywood", weight=3]; 928[label="vuu310/EQ",fontsize=10,color="white",style="solid",shape="box"];64 -> 928[label="",style="solid", color="burlywood", weight=9]; 928 -> 109[label="",style="solid", color="burlywood", weight=3]; 929[label="vuu310/GT",fontsize=10,color="white",style="solid",shape="box"];64 -> 929[label="",style="solid", color="burlywood", weight=9]; 929 -> 110[label="",style="solid", color="burlywood", weight=3]; 65[label="primEqDouble vuu30 vuu310",fontsize=16,color="burlywood",shape="box"];930[label="vuu30/Double vuu300 vuu301",fontsize=10,color="white",style="solid",shape="box"];65 -> 930[label="",style="solid", color="burlywood", weight=9]; 930 -> 111[label="",style="solid", color="burlywood", weight=3]; 66[label="(==) vuu300 :% vuu301 vuu310",fontsize=16,color="burlywood",shape="box"];931[label="vuu310/vuu3100 :% vuu3101",fontsize=10,color="white",style="solid",shape="box"];66 -> 931[label="",style="solid", color="burlywood", weight=9]; 931 -> 112[label="",style="solid", color="burlywood", weight=3]; 67[label="primEqInt vuu30 vuu310",fontsize=16,color="burlywood",shape="triangle"];932[label="vuu30/Pos vuu300",fontsize=10,color="white",style="solid",shape="box"];67 -> 932[label="",style="solid", color="burlywood", weight=9]; 932 -> 113[label="",style="solid", color="burlywood", weight=3]; 933[label="vuu30/Neg vuu300",fontsize=10,color="white",style="solid",shape="box"];67 -> 933[label="",style="solid", color="burlywood", weight=9]; 933 -> 114[label="",style="solid", color="burlywood", weight=3]; 68[label="(==) Left vuu300 vuu310",fontsize=16,color="burlywood",shape="box"];934[label="vuu310/Left vuu3100",fontsize=10,color="white",style="solid",shape="box"];68 -> 934[label="",style="solid", color="burlywood", weight=9]; 934 -> 115[label="",style="solid", color="burlywood", weight=3]; 935[label="vuu310/Right vuu3100",fontsize=10,color="white",style="solid",shape="box"];68 -> 935[label="",style="solid", color="burlywood", weight=9]; 935 -> 116[label="",style="solid", color="burlywood", weight=3]; 69[label="(==) Right vuu300 vuu310",fontsize=16,color="burlywood",shape="box"];936[label="vuu310/Left vuu3100",fontsize=10,color="white",style="solid",shape="box"];69 -> 936[label="",style="solid", color="burlywood", weight=9]; 936 -> 117[label="",style="solid", color="burlywood", weight=3]; 937[label="vuu310/Right vuu3100",fontsize=10,color="white",style="solid",shape="box"];69 -> 937[label="",style="solid", color="burlywood", weight=9]; 937 -> 118[label="",style="solid", color="burlywood", weight=3]; 70[label="primEqChar vuu30 vuu310",fontsize=16,color="burlywood",shape="box"];938[label="vuu30/Char vuu300",fontsize=10,color="white",style="solid",shape="box"];70 -> 938[label="",style="solid", color="burlywood", weight=9]; 938 -> 119[label="",style="solid", color="burlywood", weight=3]; 71[label="(==) False vuu310",fontsize=16,color="burlywood",shape="box"];939[label="vuu310/False",fontsize=10,color="white",style="solid",shape="box"];71 -> 939[label="",style="solid", color="burlywood", weight=9]; 939 -> 120[label="",style="solid", color="burlywood", weight=3]; 940[label="vuu310/True",fontsize=10,color="white",style="solid",shape="box"];71 -> 940[label="",style="solid", color="burlywood", weight=9]; 940 -> 121[label="",style="solid", color="burlywood", weight=3]; 72[label="(==) True vuu310",fontsize=16,color="burlywood",shape="box"];941[label="vuu310/False",fontsize=10,color="white",style="solid",shape="box"];72 -> 941[label="",style="solid", color="burlywood", weight=9]; 941 -> 122[label="",style="solid", color="burlywood", weight=3]; 942[label="vuu310/True",fontsize=10,color="white",style="solid",shape="box"];72 -> 942[label="",style="solid", color="burlywood", weight=9]; 942 -> 123[label="",style="solid", color="burlywood", weight=3]; 73[label="(==) (vuu300,vuu301) vuu310",fontsize=16,color="burlywood",shape="box"];943[label="vuu310/(vuu3100,vuu3101)",fontsize=10,color="white",style="solid",shape="box"];73 -> 943[label="",style="solid", color="burlywood", weight=9]; 943 -> 124[label="",style="solid", color="burlywood", weight=3]; 74[label="(==) Nothing vuu310",fontsize=16,color="burlywood",shape="box"];944[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];74 -> 944[label="",style="solid", color="burlywood", weight=9]; 944 -> 125[label="",style="solid", color="burlywood", weight=3]; 945[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];74 -> 945[label="",style="solid", color="burlywood", weight=9]; 945 -> 126[label="",style="solid", color="burlywood", weight=3]; 75[label="(==) Just vuu300 vuu310",fontsize=16,color="burlywood",shape="box"];946[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];75 -> 946[label="",style="solid", color="burlywood", weight=9]; 946 -> 127[label="",style="solid", color="burlywood", weight=3]; 947[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];75 -> 947[label="",style="solid", color="burlywood", weight=9]; 947 -> 128[label="",style="solid", color="burlywood", weight=3]; 76[label="List.groupByYs1 (==) vuu9 (vuu10 : vuu11) (span2Span0 ((==) vuu9) vuu11 ((==) vuu9) vuu10 vuu11 otherwise)",fontsize=16,color="black",shape="box"];76 -> 129[label="",style="solid", color="black", weight=3]; 77[label="List.groupByYs1 (==) vuu9 (vuu10 : vuu11) (vuu10 : span2Ys ((==) vuu9) vuu11,span2Zs ((==) vuu9) vuu11)",fontsize=16,color="black",shape="box"];77 -> 130[label="",style="solid", color="black", weight=3]; 78 -> 34[label="",style="dashed", color="red", weight=0]; 78[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];79 -> 35[label="",style="dashed", color="red", weight=0]; 79[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];80 -> 36[label="",style="dashed", color="red", weight=0]; 80[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];81 -> 37[label="",style="dashed", color="red", weight=0]; 81[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];82 -> 38[label="",style="dashed", color="red", weight=0]; 82[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];83 -> 39[label="",style="dashed", color="red", weight=0]; 83[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];84 -> 40[label="",style="dashed", color="red", weight=0]; 84[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];85 -> 41[label="",style="dashed", color="red", weight=0]; 85[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];86 -> 42[label="",style="dashed", color="red", weight=0]; 86[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];87 -> 43[label="",style="dashed", color="red", weight=0]; 87[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];88 -> 44[label="",style="dashed", color="red", weight=0]; 88[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];89 -> 45[label="",style="dashed", color="red", weight=0]; 89[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];90 -> 46[label="",style="dashed", color="red", weight=0]; 90[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];91 -> 47[label="",style="dashed", color="red", weight=0]; 91[label="(==) vuu30 vuu310",fontsize=16,color="magenta"];92[label="List.groupByZs1 (==) vuu18 (vuu19 : vuu20) (span2Span1 ((==) vuu18) vuu20 ((==) vuu18) vuu19 vuu20 False)",fontsize=16,color="black",shape="box"];92 -> 131[label="",style="solid", color="black", weight=3]; 93[label="List.groupByZs1 (==) vuu18 (vuu19 : vuu20) (span2Span1 ((==) vuu18) vuu20 ((==) vuu18) vuu19 vuu20 True)",fontsize=16,color="black",shape="box"];93 -> 132[label="",style="solid", color="black", weight=3]; 94[label="(==) () ()",fontsize=16,color="black",shape="box"];94 -> 133[label="",style="solid", color="black", weight=3]; 95[label="primEqFloat (Float vuu300 vuu301) vuu310",fontsize=16,color="burlywood",shape="box"];948[label="vuu310/Float vuu3100 vuu3101",fontsize=10,color="white",style="solid",shape="box"];95 -> 948[label="",style="solid", color="burlywood", weight=9]; 948 -> 134[label="",style="solid", color="burlywood", weight=3]; 96[label="(==) vuu300 : vuu301 vuu3100 : vuu3101",fontsize=16,color="black",shape="box"];96 -> 135[label="",style="solid", color="black", weight=3]; 97[label="(==) vuu300 : vuu301 []",fontsize=16,color="black",shape="box"];97 -> 136[label="",style="solid", color="black", weight=3]; 98[label="(==) [] vuu3100 : vuu3101",fontsize=16,color="black",shape="box"];98 -> 137[label="",style="solid", color="black", weight=3]; 99[label="(==) [] []",fontsize=16,color="black",shape="box"];99 -> 138[label="",style="solid", color="black", weight=3]; 100[label="(==) Integer vuu300 Integer vuu3100",fontsize=16,color="black",shape="box"];100 -> 139[label="",style="solid", color="black", weight=3]; 101[label="(==) (vuu300,vuu301,vuu302) (vuu3100,vuu3101,vuu3102)",fontsize=16,color="black",shape="box"];101 -> 140[label="",style="solid", color="black", weight=3]; 102[label="(==) LT LT",fontsize=16,color="black",shape="box"];102 -> 141[label="",style="solid", color="black", weight=3]; 103[label="(==) LT EQ",fontsize=16,color="black",shape="box"];103 -> 142[label="",style="solid", color="black", weight=3]; 104[label="(==) LT GT",fontsize=16,color="black",shape="box"];104 -> 143[label="",style="solid", color="black", weight=3]; 105[label="(==) EQ LT",fontsize=16,color="black",shape="box"];105 -> 144[label="",style="solid", color="black", weight=3]; 106[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];106 -> 145[label="",style="solid", color="black", weight=3]; 107[label="(==) EQ GT",fontsize=16,color="black",shape="box"];107 -> 146[label="",style="solid", color="black", weight=3]; 108[label="(==) GT LT",fontsize=16,color="black",shape="box"];108 -> 147[label="",style="solid", color="black", weight=3]; 109[label="(==) GT EQ",fontsize=16,color="black",shape="box"];109 -> 148[label="",style="solid", color="black", weight=3]; 110[label="(==) GT GT",fontsize=16,color="black",shape="box"];110 -> 149[label="",style="solid", color="black", weight=3]; 111[label="primEqDouble (Double vuu300 vuu301) vuu310",fontsize=16,color="burlywood",shape="box"];949[label="vuu310/Double vuu3100 vuu3101",fontsize=10,color="white",style="solid",shape="box"];111 -> 949[label="",style="solid", color="burlywood", weight=9]; 949 -> 150[label="",style="solid", color="burlywood", weight=3]; 112[label="(==) vuu300 :% vuu301 vuu3100 :% vuu3101",fontsize=16,color="black",shape="box"];112 -> 151[label="",style="solid", color="black", weight=3]; 113[label="primEqInt (Pos vuu300) vuu310",fontsize=16,color="burlywood",shape="box"];950[label="vuu300/Succ vuu3000",fontsize=10,color="white",style="solid",shape="box"];113 -> 950[label="",style="solid", color="burlywood", weight=9]; 950 -> 152[label="",style="solid", color="burlywood", weight=3]; 951[label="vuu300/Zero",fontsize=10,color="white",style="solid",shape="box"];113 -> 951[label="",style="solid", color="burlywood", weight=9]; 951 -> 153[label="",style="solid", color="burlywood", weight=3]; 114[label="primEqInt (Neg vuu300) vuu310",fontsize=16,color="burlywood",shape="box"];952[label="vuu300/Succ vuu3000",fontsize=10,color="white",style="solid",shape="box"];114 -> 952[label="",style="solid", color="burlywood", weight=9]; 952 -> 154[label="",style="solid", color="burlywood", weight=3]; 953[label="vuu300/Zero",fontsize=10,color="white",style="solid",shape="box"];114 -> 953[label="",style="solid", color="burlywood", weight=9]; 953 -> 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970[label="",style="solid", color="blue", weight=9]; 970 -> 204[label="",style="solid", color="blue", weight=3]; 971[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 971[label="",style="solid", color="blue", weight=9]; 971 -> 205[label="",style="solid", color="blue", weight=3]; 972[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 972[label="",style="solid", color="blue", weight=9]; 972 -> 206[label="",style="solid", color="blue", weight=3]; 973[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 973[label="",style="solid", color="blue", weight=9]; 973 -> 207[label="",style="solid", color="blue", weight=3]; 974[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 974[label="",style="solid", color="blue", weight=9]; 974 -> 208[label="",style="solid", color="blue", weight=3]; 975[label="== :: ((@2) a 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221[label="",style="solid", color="blue", weight=3]; 988[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];159 -> 988[label="",style="solid", color="blue", weight=9]; 988 -> 222[label="",style="solid", color="blue", weight=3]; 989[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];159 -> 989[label="",style="solid", color="blue", weight=9]; 989 -> 223[label="",style="solid", color="blue", weight=3]; 990[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];159 -> 990[label="",style="solid", color="blue", weight=9]; 990 -> 224[label="",style="solid", color="blue", weight=3]; 160[label="primEqChar (Char vuu300) (Char vuu3100)",fontsize=16,color="black",shape="box"];160 -> 225[label="",style="solid", color="black", weight=3]; 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1036[label="",style="solid", color="blue", weight=9]; 1036 -> 298[label="",style="solid", color="blue", weight=3]; 254[label="vuu301 == vuu3101",fontsize=16,color="blue",shape="box"];1037[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];254 -> 1037[label="",style="solid", color="blue", weight=9]; 1037 -> 299[label="",style="solid", color="blue", weight=3]; 1038[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];254 -> 1038[label="",style="solid", color="blue", weight=9]; 1038 -> 300[label="",style="solid", color="blue", weight=3]; 189[label="primEqInt (Pos (Succ vuu3000)) (Pos vuu3100)",fontsize=16,color="burlywood",shape="box"];1039[label="vuu3100/Succ vuu31000",fontsize=10,color="white",style="solid",shape="box"];189 -> 1039[label="",style="solid", color="burlywood", weight=9]; 1039 -> 301[label="",style="solid", color="burlywood", weight=3]; 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313[label="",style="solid", color="burlywood", weight=3]; 1050[label="vuu3100/Zero",fontsize=10,color="white",style="solid",shape="box"];196 -> 1050[label="",style="solid", color="burlywood", weight=9]; 1050 -> 314[label="",style="solid", color="burlywood", weight=3]; 197 -> 34[label="",style="dashed", color="red", weight=0]; 197[label="vuu300 == vuu3100",fontsize=16,color="magenta"];197 -> 315[label="",style="dashed", color="magenta", weight=3]; 197 -> 316[label="",style="dashed", color="magenta", weight=3]; 198 -> 35[label="",style="dashed", color="red", weight=0]; 198[label="vuu300 == vuu3100",fontsize=16,color="magenta"];198 -> 317[label="",style="dashed", color="magenta", weight=3]; 198 -> 318[label="",style="dashed", color="magenta", weight=3]; 199 -> 36[label="",style="dashed", color="red", weight=0]; 199[label="vuu300 == vuu3100",fontsize=16,color="magenta"];199 -> 319[label="",style="dashed", color="magenta", weight=3]; 199 -> 320[label="",style="dashed", color="magenta", 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45[label="",style="dashed", color="red", weight=0]; 208[label="vuu300 == vuu3100",fontsize=16,color="magenta"];208 -> 337[label="",style="dashed", color="magenta", weight=3]; 208 -> 338[label="",style="dashed", color="magenta", weight=3]; 209 -> 46[label="",style="dashed", color="red", weight=0]; 209[label="vuu300 == vuu3100",fontsize=16,color="magenta"];209 -> 339[label="",style="dashed", color="magenta", weight=3]; 209 -> 340[label="",style="dashed", color="magenta", weight=3]; 210 -> 47[label="",style="dashed", color="red", weight=0]; 210[label="vuu300 == vuu3100",fontsize=16,color="magenta"];210 -> 341[label="",style="dashed", color="magenta", weight=3]; 210 -> 342[label="",style="dashed", color="magenta", weight=3]; 211 -> 34[label="",style="dashed", color="red", weight=0]; 211[label="vuu300 == vuu3100",fontsize=16,color="magenta"];211 -> 343[label="",style="dashed", color="magenta", weight=3]; 211 -> 344[label="",style="dashed", color="magenta", weight=3]; 212 -> 35[label="",style="dashed", color="red", weight=0]; 212[label="vuu300 == vuu3100",fontsize=16,color="magenta"];212 -> 345[label="",style="dashed", color="magenta", weight=3]; 212 -> 346[label="",style="dashed", color="magenta", weight=3]; 213 -> 36[label="",style="dashed", color="red", weight=0]; 213[label="vuu300 == vuu3100",fontsize=16,color="magenta"];213 -> 347[label="",style="dashed", color="magenta", weight=3]; 213 -> 348[label="",style="dashed", color="magenta", weight=3]; 214 -> 37[label="",style="dashed", color="red", weight=0]; 214[label="vuu300 == vuu3100",fontsize=16,color="magenta"];214 -> 349[label="",style="dashed", color="magenta", weight=3]; 214 -> 350[label="",style="dashed", color="magenta", weight=3]; 215 -> 38[label="",style="dashed", color="red", weight=0]; 215[label="vuu300 == vuu3100",fontsize=16,color="magenta"];215 -> 351[label="",style="dashed", color="magenta", weight=3]; 215 -> 352[label="",style="dashed", color="magenta", weight=3]; 216 -> 39[label="",style="dashed", color="red", weight=0]; 216[label="vuu300 == vuu3100",fontsize=16,color="magenta"];216 -> 353[label="",style="dashed", color="magenta", weight=3]; 216 -> 354[label="",style="dashed", color="magenta", weight=3]; 217 -> 40[label="",style="dashed", color="red", weight=0]; 217[label="vuu300 == vuu3100",fontsize=16,color="magenta"];217 -> 355[label="",style="dashed", color="magenta", weight=3]; 217 -> 356[label="",style="dashed", color="magenta", weight=3]; 218 -> 41[label="",style="dashed", color="red", weight=0]; 218[label="vuu300 == vuu3100",fontsize=16,color="magenta"];218 -> 357[label="",style="dashed", color="magenta", weight=3]; 218 -> 358[label="",style="dashed", color="magenta", weight=3]; 219 -> 42[label="",style="dashed", color="red", weight=0]; 219[label="vuu300 == vuu3100",fontsize=16,color="magenta"];219 -> 359[label="",style="dashed", color="magenta", weight=3]; 219 -> 360[label="",style="dashed", color="magenta", weight=3]; 220 -> 43[label="",style="dashed", color="red", weight=0]; 220[label="vuu300 == vuu3100",fontsize=16,color="magenta"];220 -> 361[label="",style="dashed", color="magenta", weight=3]; 220 -> 362[label="",style="dashed", color="magenta", weight=3]; 221 -> 44[label="",style="dashed", color="red", weight=0]; 221[label="vuu300 == vuu3100",fontsize=16,color="magenta"];221 -> 363[label="",style="dashed", color="magenta", weight=3]; 221 -> 364[label="",style="dashed", color="magenta", weight=3]; 222 -> 45[label="",style="dashed", color="red", weight=0]; 222[label="vuu300 == vuu3100",fontsize=16,color="magenta"];222 -> 365[label="",style="dashed", color="magenta", weight=3]; 222 -> 366[label="",style="dashed", color="magenta", weight=3]; 223 -> 46[label="",style="dashed", color="red", weight=0]; 223[label="vuu300 == vuu3100",fontsize=16,color="magenta"];223 -> 367[label="",style="dashed", color="magenta", weight=3]; 223 -> 368[label="",style="dashed", color="magenta", weight=3]; 224 -> 47[label="",style="dashed", color="red", weight=0]; 224[label="vuu300 == vuu3100",fontsize=16,color="magenta"];224 -> 369[label="",style="dashed", color="magenta", weight=3]; 224 -> 370[label="",style="dashed", color="magenta", weight=3]; 225[label="primEqNat vuu300 vuu3100",fontsize=16,color="burlywood",shape="triangle"];1051[label="vuu300/Succ vuu3000",fontsize=10,color="white",style="solid",shape="box"];225 -> 1051[label="",style="solid", color="burlywood", weight=9]; 1051 -> 371[label="",style="solid", color="burlywood", weight=3]; 1052[label="vuu300/Zero",fontsize=10,color="white",style="solid",shape="box"];225 -> 1052[label="",style="solid", color="burlywood", weight=9]; 1052 -> 372[label="",style="solid", color="burlywood", weight=3]; 255[label="vuu300 == vuu3100",fontsize=16,color="blue",shape="box"];1053[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1053[label="",style="solid", color="blue", weight=9]; 1053 -> 373[label="",style="solid", color="blue", weight=3]; 1054[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1054[label="",style="solid", color="blue", weight=9]; 1054 -> 374[label="",style="solid", color="blue", weight=3]; 1055[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1055[label="",style="solid", color="blue", weight=9]; 1055 -> 375[label="",style="solid", color="blue", weight=3]; 1056[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1056[label="",style="solid", color="blue", weight=9]; 1056 -> 376[label="",style="solid", color="blue", weight=3]; 1057[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1057[label="",style="solid", color="blue", weight=9]; 1057 -> 377[label="",style="solid", color="blue", weight=3]; 1058[label="== :: Ordering -> Ordering -> 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weight=9]; 1062 -> 382[label="",style="solid", color="blue", weight=3]; 1063[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1063[label="",style="solid", color="blue", weight=9]; 1063 -> 383[label="",style="solid", color="blue", weight=3]; 1064[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1064[label="",style="solid", color="blue", weight=9]; 1064 -> 384[label="",style="solid", color="blue", weight=3]; 1065[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1065[label="",style="solid", color="blue", weight=9]; 1065 -> 385[label="",style="solid", color="blue", weight=3]; 1066[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 1066[label="",style="solid", color="blue", weight=9]; 1066 -> 386[label="",style="solid", color="blue", weight=3]; 256[label="vuu301 == 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315[label="vuu300",fontsize=16,color="green",shape="box"];316[label="vuu3100",fontsize=16,color="green",shape="box"];317[label="vuu300",fontsize=16,color="green",shape="box"];318[label="vuu3100",fontsize=16,color="green",shape="box"];319[label="vuu300",fontsize=16,color="green",shape="box"];320[label="vuu3100",fontsize=16,color="green",shape="box"];321[label="vuu300",fontsize=16,color="green",shape="box"];322[label="vuu3100",fontsize=16,color="green",shape="box"];323[label="vuu300",fontsize=16,color="green",shape="box"];324[label="vuu3100",fontsize=16,color="green",shape="box"];325[label="vuu300",fontsize=16,color="green",shape="box"];326[label="vuu3100",fontsize=16,color="green",shape="box"];327[label="vuu300",fontsize=16,color="green",shape="box"];328[label="vuu3100",fontsize=16,color="green",shape="box"];329[label="vuu300",fontsize=16,color="green",shape="box"];330[label="vuu3100",fontsize=16,color="green",shape="box"];331[label="vuu300",fontsize=16,color="green",shape="box"];332[label="vuu3100",fontsize=16,color="green",shape="box"];333[label="vuu300",fontsize=16,color="green",shape="box"];334[label="vuu3100",fontsize=16,color="green",shape="box"];335[label="vuu300",fontsize=16,color="green",shape="box"];336[label="vuu3100",fontsize=16,color="green",shape="box"];337[label="vuu300",fontsize=16,color="green",shape="box"];338[label="vuu3100",fontsize=16,color="green",shape="box"];339[label="vuu300",fontsize=16,color="green",shape="box"];340[label="vuu3100",fontsize=16,color="green",shape="box"];341[label="vuu300",fontsize=16,color="green",shape="box"];342[label="vuu3100",fontsize=16,color="green",shape="box"];343[label="vuu300",fontsize=16,color="green",shape="box"];344[label="vuu3100",fontsize=16,color="green",shape="box"];345[label="vuu300",fontsize=16,color="green",shape="box"];346[label="vuu3100",fontsize=16,color="green",shape="box"];347[label="vuu300",fontsize=16,color="green",shape="box"];348[label="vuu3100",fontsize=16,color="green",shape="box"];349[label="vuu300",fontsize=16,color="green",shape="box"];350[label="vuu3100",fontsize=16,color="green",shape="box"];351[label="vuu300",fontsize=16,color="green",shape="box"];352[label="vuu3100",fontsize=16,color="green",shape="box"];353[label="vuu300",fontsize=16,color="green",shape="box"];354[label="vuu3100",fontsize=16,color="green",shape="box"];355[label="vuu300",fontsize=16,color="green",shape="box"];356[label="vuu3100",fontsize=16,color="green",shape="box"];357[label="vuu300",fontsize=16,color="green",shape="box"];358[label="vuu3100",fontsize=16,color="green",shape="box"];359[label="vuu300",fontsize=16,color="green",shape="box"];360[label="vuu3100",fontsize=16,color="green",shape="box"];361[label="vuu300",fontsize=16,color="green",shape="box"];362[label="vuu3100",fontsize=16,color="green",shape="box"];363[label="vuu300",fontsize=16,color="green",shape="box"];364[label="vuu3100",fontsize=16,color="green",shape="box"];365[label="vuu300",fontsize=16,color="green",shape="box"];366[label="vuu3100",fontsize=16,color="green",shape="box"];367[label="vuu300",fontsize=16,color="green",shape="box"];368[label="vuu3100",fontsize=16,color="green",shape="box"];369[label="vuu300",fontsize=16,color="green",shape="box"];370[label="vuu3100",fontsize=16,color="green",shape="box"];371[label="primEqNat 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weight=3]; 373 -> 34[label="",style="dashed", color="red", weight=0]; 373[label="vuu300 == vuu3100",fontsize=16,color="magenta"];373 -> 549[label="",style="dashed", color="magenta", weight=3]; 373 -> 550[label="",style="dashed", color="magenta", weight=3]; 374 -> 35[label="",style="dashed", color="red", weight=0]; 374[label="vuu300 == vuu3100",fontsize=16,color="magenta"];374 -> 551[label="",style="dashed", color="magenta", weight=3]; 374 -> 552[label="",style="dashed", color="magenta", weight=3]; 375 -> 36[label="",style="dashed", color="red", weight=0]; 375[label="vuu300 == vuu3100",fontsize=16,color="magenta"];375 -> 553[label="",style="dashed", color="magenta", weight=3]; 375 -> 554[label="",style="dashed", color="magenta", weight=3]; 376 -> 37[label="",style="dashed", color="red", weight=0]; 376[label="vuu300 == vuu3100",fontsize=16,color="magenta"];376 -> 555[label="",style="dashed", color="magenta", weight=3]; 376 -> 556[label="",style="dashed", color="magenta", weight=3]; 377 -> 38[label="",style="dashed", color="red", weight=0]; 377[label="vuu300 == vuu3100",fontsize=16,color="magenta"];377 -> 557[label="",style="dashed", color="magenta", weight=3]; 377 -> 558[label="",style="dashed", color="magenta", weight=3]; 378 -> 39[label="",style="dashed", color="red", weight=0]; 378[label="vuu300 == vuu3100",fontsize=16,color="magenta"];378 -> 559[label="",style="dashed", color="magenta", weight=3]; 378 -> 560[label="",style="dashed", color="magenta", weight=3]; 379 -> 40[label="",style="dashed", color="red", weight=0]; 379[label="vuu300 == vuu3100",fontsize=16,color="magenta"];379 -> 561[label="",style="dashed", color="magenta", weight=3]; 379 -> 562[label="",style="dashed", color="magenta", weight=3]; 380 -> 41[label="",style="dashed", color="red", weight=0]; 380[label="vuu300 == vuu3100",fontsize=16,color="magenta"];380 -> 563[label="",style="dashed", color="magenta", weight=3]; 380 -> 564[label="",style="dashed", color="magenta", weight=3]; 381 -> 42[label="",style="dashed", color="red", weight=0]; 381[label="vuu300 == vuu3100",fontsize=16,color="magenta"];381 -> 565[label="",style="dashed", color="magenta", weight=3]; 381 -> 566[label="",style="dashed", color="magenta", weight=3]; 382 -> 43[label="",style="dashed", color="red", weight=0]; 382[label="vuu300 == vuu3100",fontsize=16,color="magenta"];382 -> 567[label="",style="dashed", color="magenta", weight=3]; 382 -> 568[label="",style="dashed", color="magenta", weight=3]; 383 -> 44[label="",style="dashed", color="red", weight=0]; 383[label="vuu300 == vuu3100",fontsize=16,color="magenta"];383 -> 569[label="",style="dashed", color="magenta", weight=3]; 383 -> 570[label="",style="dashed", color="magenta", weight=3]; 384 -> 45[label="",style="dashed", color="red", weight=0]; 384[label="vuu300 == vuu3100",fontsize=16,color="magenta"];384 -> 571[label="",style="dashed", color="magenta", weight=3]; 384 -> 572[label="",style="dashed", color="magenta", weight=3]; 385 -> 46[label="",style="dashed", color="red", weight=0]; 385[label="vuu300 == vuu3100",fontsize=16,color="magenta"];385 -> 573[label="",style="dashed", color="magenta", weight=3]; 385 -> 574[label="",style="dashed", color="magenta", weight=3]; 386 -> 47[label="",style="dashed", color="red", weight=0]; 386[label="vuu300 == vuu3100",fontsize=16,color="magenta"];386 -> 575[label="",style="dashed", color="magenta", weight=3]; 386 -> 576[label="",style="dashed", color="magenta", weight=3]; 387 -> 34[label="",style="dashed", color="red", weight=0]; 387[label="vuu301 == vuu3101",fontsize=16,color="magenta"];387 -> 577[label="",style="dashed", color="magenta", weight=3]; 387 -> 578[label="",style="dashed", color="magenta", weight=3]; 388 -> 35[label="",style="dashed", color="red", weight=0]; 388[label="vuu301 == vuu3101",fontsize=16,color="magenta"];388 -> 579[label="",style="dashed", color="magenta", weight=3]; 388 -> 580[label="",style="dashed", color="magenta", weight=3]; 389 -> 36[label="",style="dashed", color="red", weight=0]; 389[label="vuu301 == vuu3101",fontsize=16,color="magenta"];389 -> 581[label="",style="dashed", color="magenta", weight=3]; 389 -> 582[label="",style="dashed", color="magenta", weight=3]; 390 -> 37[label="",style="dashed", color="red", weight=0]; 390[label="vuu301 == vuu3101",fontsize=16,color="magenta"];390 -> 583[label="",style="dashed", color="magenta", weight=3]; 390 -> 584[label="",style="dashed", color="magenta", weight=3]; 391 -> 38[label="",style="dashed", color="red", weight=0]; 391[label="vuu301 == vuu3101",fontsize=16,color="magenta"];391 -> 585[label="",style="dashed", color="magenta", weight=3]; 391 -> 586[label="",style="dashed", color="magenta", weight=3]; 392 -> 39[label="",style="dashed", color="red", weight=0]; 392[label="vuu301 == vuu3101",fontsize=16,color="magenta"];392 -> 587[label="",style="dashed", color="magenta", weight=3]; 392 -> 588[label="",style="dashed", color="magenta", weight=3]; 393 -> 40[label="",style="dashed", color="red", weight=0]; 393[label="vuu301 == vuu3101",fontsize=16,color="magenta"];393 -> 589[label="",style="dashed", color="magenta", weight=3]; 393 -> 590[label="",style="dashed", color="magenta", weight=3]; 394 -> 41[label="",style="dashed", color="red", weight=0]; 394[label="vuu301 == vuu3101",fontsize=16,color="magenta"];394 -> 591[label="",style="dashed", color="magenta", weight=3]; 394 -> 592[label="",style="dashed", color="magenta", weight=3]; 395 -> 42[label="",style="dashed", color="red", weight=0]; 395[label="vuu301 == vuu3101",fontsize=16,color="magenta"];395 -> 593[label="",style="dashed", color="magenta", weight=3]; 395 -> 594[label="",style="dashed", color="magenta", weight=3]; 396 -> 43[label="",style="dashed", color="red", weight=0]; 396[label="vuu301 == vuu3101",fontsize=16,color="magenta"];396 -> 595[label="",style="dashed", color="magenta", weight=3]; 396 -> 596[label="",style="dashed", color="magenta", weight=3]; 397 -> 44[label="",style="dashed", color="red", weight=0]; 397[label="vuu301 == vuu3101",fontsize=16,color="magenta"];397 -> 597[label="",style="dashed", color="magenta", weight=3]; 397 -> 598[label="",style="dashed", color="magenta", weight=3]; 398 -> 45[label="",style="dashed", color="red", weight=0]; 398[label="vuu301 == vuu3101",fontsize=16,color="magenta"];398 -> 599[label="",style="dashed", color="magenta", weight=3]; 398 -> 600[label="",style="dashed", color="magenta", weight=3]; 399 -> 46[label="",style="dashed", color="red", weight=0]; 399[label="vuu301 == vuu3101",fontsize=16,color="magenta"];399 -> 601[label="",style="dashed", color="magenta", weight=3]; 399 -> 602[label="",style="dashed", color="magenta", weight=3]; 400 -> 47[label="",style="dashed", color="red", weight=0]; 400[label="vuu301 == vuu3101",fontsize=16,color="magenta"];400 -> 603[label="",style="dashed", color="magenta", weight=3]; 400 -> 604[label="",style="dashed", color="magenta", weight=3]; 401[label="vuu300",fontsize=16,color="green",shape="box"];402[label="vuu3100",fontsize=16,color="green",shape="box"];403[label="vuu300",fontsize=16,color="green",shape="box"];404[label="vuu3100",fontsize=16,color="green",shape="box"];405[label="vuu300",fontsize=16,color="green",shape="box"];406[label="vuu3100",fontsize=16,color="green",shape="box"];407[label="vuu300",fontsize=16,color="green",shape="box"];408[label="vuu3100",fontsize=16,color="green",shape="box"];409[label="vuu300",fontsize=16,color="green",shape="box"];410[label="vuu3100",fontsize=16,color="green",shape="box"];411[label="vuu300",fontsize=16,color="green",shape="box"];412[label="vuu3100",fontsize=16,color="green",shape="box"];413[label="vuu300",fontsize=16,color="green",shape="box"];414[label="vuu3100",fontsize=16,color="green",shape="box"];415[label="vuu300",fontsize=16,color="green",shape="box"];416[label="vuu3100",fontsize=16,color="green",shape="box"];417[label="vuu300",fontsize=16,color="green",shape="box"];418[label="vuu3100",fontsize=16,color="green",shape="box"];419[label="vuu300",fontsize=16,color="green",shape="box"];420[label="vuu3100",fontsize=16,color="green",shape="box"];421[label="vuu300",fontsize=16,color="green",shape="box"];422[label="vuu3100",fontsize=16,color="green",shape="box"];423[label="vuu300",fontsize=16,color="green",shape="box"];424[label="vuu3100",fontsize=16,color="green",shape="box"];425[label="vuu300",fontsize=16,color="green",shape="box"];426[label="vuu3100",fontsize=16,color="green",shape="box"];427[label="vuu300",fontsize=16,color="green",shape="box"];428[label="vuu3100",fontsize=16,color="green",shape="box"];429[label="span2Ys0 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1116[label="",style="solid", color="burlywood", weight=9]; 1116 -> 608[label="",style="solid", color="burlywood", weight=3]; 432[label="primMulInt vuu300 vuu3101",fontsize=16,color="burlywood",shape="box"];1117[label="vuu300/Pos vuu3000",fontsize=10,color="white",style="solid",shape="box"];432 -> 1117[label="",style="solid", color="burlywood", weight=9]; 1117 -> 609[label="",style="solid", color="burlywood", weight=3]; 1118[label="vuu300/Neg vuu3000",fontsize=10,color="white",style="solid",shape="box"];432 -> 1118[label="",style="solid", color="burlywood", weight=9]; 1118 -> 610[label="",style="solid", color="burlywood", weight=3]; 433[label="vuu301",fontsize=16,color="green",shape="box"];434[label="vuu3100",fontsize=16,color="green",shape="box"];435[label="vuu300",fontsize=16,color="green",shape="box"];436[label="vuu3100",fontsize=16,color="green",shape="box"];437[label="vuu300",fontsize=16,color="green",shape="box"];438[label="vuu3100",fontsize=16,color="green",shape="box"];439[label="vuu300",fontsize=16,color="green",shape="box"];440[label="vuu3100",fontsize=16,color="green",shape="box"];441[label="vuu300",fontsize=16,color="green",shape="box"];442[label="vuu3100",fontsize=16,color="green",shape="box"];443[label="vuu300",fontsize=16,color="green",shape="box"];444[label="vuu3100",fontsize=16,color="green",shape="box"];445[label="vuu300",fontsize=16,color="green",shape="box"];446[label="vuu3100",fontsize=16,color="green",shape="box"];447[label="vuu300",fontsize=16,color="green",shape="box"];448[label="vuu3100",fontsize=16,color="green",shape="box"];449[label="vuu300",fontsize=16,color="green",shape="box"];450[label="vuu3100",fontsize=16,color="green",shape="box"];451[label="vuu300",fontsize=16,color="green",shape="box"];452[label="vuu3100",fontsize=16,color="green",shape="box"];453[label="vuu300",fontsize=16,color="green",shape="box"];454[label="vuu3100",fontsize=16,color="green",shape="box"];455[label="vuu300",fontsize=16,color="green",shape="box"];456[label="vuu3100",fontsize=16,color="green",shape="box"];457[label="vuu300",fontsize=16,color="green",shape="box"];458[label="vuu3100",fontsize=16,color="green",shape="box"];459[label="vuu300",fontsize=16,color="green",shape="box"];460[label="vuu3100",fontsize=16,color="green",shape="box"];461[label="vuu300",fontsize=16,color="green",shape="box"];462[label="vuu3100",fontsize=16,color="green",shape="box"];463[label="False",fontsize=16,color="green",shape="box"];464[label="vuu27",fontsize=16,color="green",shape="box"];465[label="vuu300",fontsize=16,color="green",shape="box"];466[label="vuu3100",fontsize=16,color="green",shape="box"];467[label="vuu300",fontsize=16,color="green",shape="box"];468[label="vuu3100",fontsize=16,color="green",shape="box"];469[label="vuu300",fontsize=16,color="green",shape="box"];470[label="vuu3100",fontsize=16,color="green",shape="box"];471[label="vuu300",fontsize=16,color="green",shape="box"];472[label="vuu3100",fontsize=16,color="green",shape="box"];473[label="vuu300",fontsize=16,color="green",shape="box"];474[label="vuu3100",fontsize=16,color="green",shape="box"];475[label="vuu300",fontsize=16,color="green",shape="box"];476[label="vuu3100",fontsize=16,color="green",shape="box"];477[label="vuu300",fontsize=16,color="green",shape="box"];478[label="vuu3100",fontsize=16,color="green",shape="box"];479[label="vuu300",fontsize=16,color="green",shape="box"];480[label="vuu3100",fontsize=16,color="green",shape="box"];481[label="vuu300",fontsize=16,color="green",shape="box"];482[label="vuu3100",fontsize=16,color="green",shape="box"];483[label="vuu300",fontsize=16,color="green",shape="box"];484[label="vuu3100",fontsize=16,color="green",shape="box"];485[label="vuu300",fontsize=16,color="green",shape="box"];486[label="vuu3100",fontsize=16,color="green",shape="box"];487[label="vuu300",fontsize=16,color="green",shape="box"];488[label="vuu3100",fontsize=16,color="green",shape="box"];489[label="vuu300",fontsize=16,color="green",shape="box"];490[label="vuu3100",fontsize=16,color="green",shape="box"];491[label="vuu300",fontsize=16,color="green",shape="box"];492[label="vuu3100",fontsize=16,color="green",shape="box"];493 -> 34[label="",style="dashed", color="red", weight=0]; 493[label="vuu301 == vuu3101",fontsize=16,color="magenta"];493 -> 611[label="",style="dashed", color="magenta", weight=3]; 493 -> 612[label="",style="dashed", color="magenta", weight=3]; 494 -> 35[label="",style="dashed", color="red", weight=0]; 494[label="vuu301 == vuu3101",fontsize=16,color="magenta"];494 -> 613[label="",style="dashed", color="magenta", weight=3]; 494 -> 614[label="",style="dashed", color="magenta", weight=3]; 495 -> 36[label="",style="dashed", color="red", weight=0]; 495[label="vuu301 == vuu3101",fontsize=16,color="magenta"];495 -> 615[label="",style="dashed", color="magenta", weight=3]; 495 -> 616[label="",style="dashed", color="magenta", weight=3]; 496 -> 37[label="",style="dashed", color="red", weight=0]; 496[label="vuu301 == vuu3101",fontsize=16,color="magenta"];496 -> 617[label="",style="dashed", color="magenta", weight=3]; 496 -> 618[label="",style="dashed", color="magenta", weight=3]; 497 -> 38[label="",style="dashed", color="red", weight=0]; 497[label="vuu301 == vuu3101",fontsize=16,color="magenta"];497 -> 619[label="",style="dashed", color="magenta", weight=3]; 497 -> 620[label="",style="dashed", color="magenta", weight=3]; 498 -> 39[label="",style="dashed", color="red", weight=0]; 498[label="vuu301 == vuu3101",fontsize=16,color="magenta"];498 -> 621[label="",style="dashed", color="magenta", weight=3]; 498 -> 622[label="",style="dashed", color="magenta", weight=3]; 499 -> 40[label="",style="dashed", color="red", weight=0]; 499[label="vuu301 == vuu3101",fontsize=16,color="magenta"];499 -> 623[label="",style="dashed", color="magenta", weight=3]; 499 -> 624[label="",style="dashed", color="magenta", weight=3]; 500 -> 41[label="",style="dashed", color="red", weight=0]; 500[label="vuu301 == vuu3101",fontsize=16,color="magenta"];500 -> 625[label="",style="dashed", color="magenta", weight=3]; 500 -> 626[label="",style="dashed", color="magenta", weight=3]; 501 -> 42[label="",style="dashed", color="red", weight=0]; 501[label="vuu301 == vuu3101",fontsize=16,color="magenta"];501 -> 627[label="",style="dashed", color="magenta", weight=3]; 501 -> 628[label="",style="dashed", color="magenta", weight=3]; 502 -> 43[label="",style="dashed", color="red", weight=0]; 502[label="vuu301 == vuu3101",fontsize=16,color="magenta"];502 -> 629[label="",style="dashed", color="magenta", weight=3]; 502 -> 630[label="",style="dashed", color="magenta", weight=3]; 503 -> 44[label="",style="dashed", color="red", weight=0]; 503[label="vuu301 == vuu3101",fontsize=16,color="magenta"];503 -> 631[label="",style="dashed", color="magenta", weight=3]; 503 -> 632[label="",style="dashed", color="magenta", weight=3]; 504 -> 45[label="",style="dashed", color="red", weight=0]; 504[label="vuu301 == vuu3101",fontsize=16,color="magenta"];504 -> 633[label="",style="dashed", color="magenta", weight=3]; 504 -> 634[label="",style="dashed", color="magenta", weight=3]; 505 -> 46[label="",style="dashed", color="red", weight=0]; 505[label="vuu301 == vuu3101",fontsize=16,color="magenta"];505 -> 635[label="",style="dashed", color="magenta", weight=3]; 505 -> 636[label="",style="dashed", color="magenta", weight=3]; 506 -> 47[label="",style="dashed", color="red", weight=0]; 506[label="vuu301 == vuu3101",fontsize=16,color="magenta"];506 -> 637[label="",style="dashed", color="magenta", weight=3]; 506 -> 638[label="",style="dashed", color="magenta", weight=3]; 507 -> 34[label="",style="dashed", color="red", weight=0]; 507[label="vuu302 == vuu3102",fontsize=16,color="magenta"];507 -> 639[label="",style="dashed", color="magenta", weight=3]; 507 -> 640[label="",style="dashed", color="magenta", weight=3]; 508 -> 35[label="",style="dashed", color="red", weight=0]; 508[label="vuu302 == vuu3102",fontsize=16,color="magenta"];508 -> 641[label="",style="dashed", color="magenta", weight=3]; 508 -> 642[label="",style="dashed", color="magenta", weight=3]; 509 -> 36[label="",style="dashed", color="red", weight=0]; 509[label="vuu302 == vuu3102",fontsize=16,color="magenta"];509 -> 643[label="",style="dashed", color="magenta", weight=3]; 509 -> 644[label="",style="dashed", color="magenta", weight=3]; 510 -> 37[label="",style="dashed", color="red", weight=0]; 510[label="vuu302 == vuu3102",fontsize=16,color="magenta"];510 -> 645[label="",style="dashed", color="magenta", weight=3]; 510 -> 646[label="",style="dashed", color="magenta", weight=3]; 511 -> 38[label="",style="dashed", color="red", weight=0]; 511[label="vuu302 == vuu3102",fontsize=16,color="magenta"];511 -> 647[label="",style="dashed", color="magenta", weight=3]; 511 -> 648[label="",style="dashed", color="magenta", weight=3]; 512 -> 39[label="",style="dashed", color="red", weight=0]; 512[label="vuu302 == vuu3102",fontsize=16,color="magenta"];512 -> 649[label="",style="dashed", color="magenta", weight=3]; 512 -> 650[label="",style="dashed", color="magenta", weight=3]; 513 -> 40[label="",style="dashed", color="red", weight=0]; 513[label="vuu302 == vuu3102",fontsize=16,color="magenta"];513 -> 651[label="",style="dashed", color="magenta", weight=3]; 513 -> 652[label="",style="dashed", color="magenta", weight=3]; 514 -> 41[label="",style="dashed", color="red", weight=0]; 514[label="vuu302 == vuu3102",fontsize=16,color="magenta"];514 -> 653[label="",style="dashed", color="magenta", weight=3]; 514 -> 654[label="",style="dashed", color="magenta", weight=3]; 515 -> 42[label="",style="dashed", color="red", weight=0]; 515[label="vuu302 == vuu3102",fontsize=16,color="magenta"];515 -> 655[label="",style="dashed", color="magenta", weight=3]; 515 -> 656[label="",style="dashed", color="magenta", weight=3]; 516 -> 43[label="",style="dashed", color="red", weight=0]; 516[label="vuu302 == vuu3102",fontsize=16,color="magenta"];516 -> 657[label="",style="dashed", color="magenta", weight=3]; 516 -> 658[label="",style="dashed", color="magenta", weight=3]; 517 -> 44[label="",style="dashed", color="red", weight=0]; 517[label="vuu302 == vuu3102",fontsize=16,color="magenta"];517 -> 659[label="",style="dashed", color="magenta", weight=3]; 517 -> 660[label="",style="dashed", color="magenta", weight=3]; 518 -> 45[label="",style="dashed", color="red", weight=0]; 518[label="vuu302 == vuu3102",fontsize=16,color="magenta"];518 -> 661[label="",style="dashed", color="magenta", weight=3]; 518 -> 662[label="",style="dashed", color="magenta", weight=3]; 519 -> 46[label="",style="dashed", color="red", weight=0]; 519[label="vuu302 == vuu3102",fontsize=16,color="magenta"];519 -> 663[label="",style="dashed", color="magenta", weight=3]; 519 -> 664[label="",style="dashed", color="magenta", weight=3]; 520 -> 47[label="",style="dashed", color="red", weight=0]; 520[label="vuu302 == vuu3102",fontsize=16,color="magenta"];520 -> 665[label="",style="dashed", color="magenta", weight=3]; 520 -> 666[label="",style="dashed", color="magenta", weight=3]; 521[label="vuu300",fontsize=16,color="green",shape="box"];522[label="vuu3101",fontsize=16,color="green",shape="box"];523[label="vuu301",fontsize=16,color="green",shape="box"];524[label="vuu3100",fontsize=16,color="green",shape="box"];525[label="vuu300",fontsize=16,color="green",shape="box"];526[label="vuu3100",fontsize=16,color="green",shape="box"];527[label="vuu300",fontsize=16,color="green",shape="box"];528[label="vuu3100",fontsize=16,color="green",shape="box"];529[label="vuu301",fontsize=16,color="green",shape="box"];530[label="vuu3101",fontsize=16,color="green",shape="box"];531[label="vuu301",fontsize=16,color="green",shape="box"];532[label="vuu3101",fontsize=16,color="green",shape="box"];533 -> 225[label="",style="dashed", color="red", weight=0]; 533[label="primEqNat vuu3000 vuu31000",fontsize=16,color="magenta"];533 -> 667[label="",style="dashed", color="magenta", weight=3]; 533 -> 668[label="",style="dashed", color="magenta", weight=3]; 534[label="False",fontsize=16,color="green",shape="box"];535[label="False",fontsize=16,color="green",shape="box"];536[label="True",fontsize=16,color="green",shape="box"];537[label="False",fontsize=16,color="green",shape="box"];538[label="True",fontsize=16,color="green",shape="box"];539 -> 225[label="",style="dashed", color="red", weight=0]; 539[label="primEqNat vuu3000 vuu31000",fontsize=16,color="magenta"];539 -> 669[label="",style="dashed", color="magenta", weight=3]; 539 -> 670[label="",style="dashed", color="magenta", weight=3]; 540[label="False",fontsize=16,color="green",shape="box"];541[label="False",fontsize=16,color="green",shape="box"];542[label="True",fontsize=16,color="green",shape="box"];543[label="False",fontsize=16,color="green",shape="box"];544[label="True",fontsize=16,color="green",shape="box"];545[label="primEqNat (Succ vuu3000) (Succ vuu31000)",fontsize=16,color="black",shape="box"];545 -> 671[label="",style="solid", color="black", weight=3]; 546[label="primEqNat (Succ vuu3000) Zero",fontsize=16,color="black",shape="box"];546 -> 672[label="",style="solid", color="black", weight=3]; 547[label="primEqNat Zero (Succ vuu31000)",fontsize=16,color="black",shape="box"];547 -> 673[label="",style="solid", color="black", weight=3]; 548[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];548 -> 674[label="",style="solid", color="black", weight=3]; 549[label="vuu300",fontsize=16,color="green",shape="box"];550[label="vuu3100",fontsize=16,color="green",shape="box"];551[label="vuu300",fontsize=16,color="green",shape="box"];552[label="vuu3100",fontsize=16,color="green",shape="box"];553[label="vuu300",fontsize=16,color="green",shape="box"];554[label="vuu3100",fontsize=16,color="green",shape="box"];555[label="vuu300",fontsize=16,color="green",shape="box"];556[label="vuu3100",fontsize=16,color="green",shape="box"];557[label="vuu300",fontsize=16,color="green",shape="box"];558[label="vuu3100",fontsize=16,color="green",shape="box"];559[label="vuu300",fontsize=16,color="green",shape="box"];560[label="vuu3100",fontsize=16,color="green",shape="box"];561[label="vuu300",fontsize=16,color="green",shape="box"];562[label="vuu3100",fontsize=16,color="green",shape="box"];563[label="vuu300",fontsize=16,color="green",shape="box"];564[label="vuu3100",fontsize=16,color="green",shape="box"];565[label="vuu300",fontsize=16,color="green",shape="box"];566[label="vuu3100",fontsize=16,color="green",shape="box"];567[label="vuu300",fontsize=16,color="green",shape="box"];568[label="vuu3100",fontsize=16,color="green",shape="box"];569[label="vuu300",fontsize=16,color="green",shape="box"];570[label="vuu3100",fontsize=16,color="green",shape="box"];571[label="vuu300",fontsize=16,color="green",shape="box"];572[label="vuu3100",fontsize=16,color="green",shape="box"];573[label="vuu300",fontsize=16,color="green",shape="box"];574[label="vuu3100",fontsize=16,color="green",shape="box"];575[label="vuu300",fontsize=16,color="green",shape="box"];576[label="vuu3100",fontsize=16,color="green",shape="box"];577[label="vuu301",fontsize=16,color="green",shape="box"];578[label="vuu3101",fontsize=16,color="green",shape="box"];579[label="vuu301",fontsize=16,color="green",shape="box"];580[label="vuu3101",fontsize=16,color="green",shape="box"];581[label="vuu301",fontsize=16,color="green",shape="box"];582[label="vuu3101",fontsize=16,color="green",shape="box"];583[label="vuu301",fontsize=16,color="green",shape="box"];584[label="vuu3101",fontsize=16,color="green",shape="box"];585[label="vuu301",fontsize=16,color="green",shape="box"];586[label="vuu3101",fontsize=16,color="green",shape="box"];587[label="vuu301",fontsize=16,color="green",shape="box"];588[label="vuu3101",fontsize=16,color="green",shape="box"];589[label="vuu301",fontsize=16,color="green",shape="box"];590[label="vuu3101",fontsize=16,color="green",shape="box"];591[label="vuu301",fontsize=16,color="green",shape="box"];592[label="vuu3101",fontsize=16,color="green",shape="box"];593[label="vuu301",fontsize=16,color="green",shape="box"];594[label="vuu3101",fontsize=16,color="green",shape="box"];595[label="vuu301",fontsize=16,color="green",shape="box"];596[label="vuu3101",fontsize=16,color="green",shape="box"];597[label="vuu301",fontsize=16,color="green",shape="box"];598[label="vuu3101",fontsize=16,color="green",shape="box"];599[label="vuu301",fontsize=16,color="green",shape="box"];600[label="vuu3101",fontsize=16,color="green",shape="box"];601[label="vuu301",fontsize=16,color="green",shape="box"];602[label="vuu3101",fontsize=16,color="green",shape="box"];603[label="vuu301",fontsize=16,color="green",shape="box"];604[label="vuu3101",fontsize=16,color="green",shape="box"];605[label="span2Ys0 ((==) vuu9) (vuu110 : vuu111) (span ((==) vuu9) (vuu110 : vuu111))",fontsize=16,color="black",shape="box"];605 -> 675[label="",style="solid", color="black", weight=3]; 606[label="span2Ys0 ((==) vuu9) [] (span ((==) vuu9) [])",fontsize=16,color="black",shape="box"];606 -> 676[label="",style="solid", color="black", weight=3]; 607[label="span2Zs0 ((==) vuu18) (vuu200 : vuu201) (span ((==) vuu18) (vuu200 : vuu201))",fontsize=16,color="black",shape="box"];607 -> 677[label="",style="solid", color="black", weight=3]; 608[label="span2Zs0 ((==) vuu18) [] (span ((==) vuu18) [])",fontsize=16,color="black",shape="box"];608 -> 678[label="",style="solid", color="black", weight=3]; 609[label="primMulInt (Pos vuu3000) vuu3101",fontsize=16,color="burlywood",shape="box"];1119[label="vuu3101/Pos vuu31010",fontsize=10,color="white",style="solid",shape="box"];609 -> 1119[label="",style="solid", color="burlywood", weight=9]; 1119 -> 679[label="",style="solid", color="burlywood", weight=3]; 1120[label="vuu3101/Neg vuu31010",fontsize=10,color="white",style="solid",shape="box"];609 -> 1120[label="",style="solid", color="burlywood", weight=9]; 1120 -> 680[label="",style="solid", color="burlywood", weight=3]; 610[label="primMulInt (Neg vuu3000) vuu3101",fontsize=16,color="burlywood",shape="box"];1121[label="vuu3101/Pos vuu31010",fontsize=10,color="white",style="solid",shape="box"];610 -> 1121[label="",style="solid", color="burlywood", weight=9]; 1121 -> 681[label="",style="solid", color="burlywood", weight=3]; 1122[label="vuu3101/Neg vuu31010",fontsize=10,color="white",style="solid",shape="box"];610 -> 1122[label="",style="solid", color="burlywood", weight=9]; 1122 -> 682[label="",style="solid", color="burlywood", weight=3]; 611[label="vuu301",fontsize=16,color="green",shape="box"];612[label="vuu3101",fontsize=16,color="green",shape="box"];613[label="vuu301",fontsize=16,color="green",shape="box"];614[label="vuu3101",fontsize=16,color="green",shape="box"];615[label="vuu301",fontsize=16,color="green",shape="box"];616[label="vuu3101",fontsize=16,color="green",shape="box"];617[label="vuu301",fontsize=16,color="green",shape="box"];618[label="vuu3101",fontsize=16,color="green",shape="box"];619[label="vuu301",fontsize=16,color="green",shape="box"];620[label="vuu3101",fontsize=16,color="green",shape="box"];621[label="vuu301",fontsize=16,color="green",shape="box"];622[label="vuu3101",fontsize=16,color="green",shape="box"];623[label="vuu301",fontsize=16,color="green",shape="box"];624[label="vuu3101",fontsize=16,color="green",shape="box"];625[label="vuu301",fontsize=16,color="green",shape="box"];626[label="vuu3101",fontsize=16,color="green",shape="box"];627[label="vuu301",fontsize=16,color="green",shape="box"];628[label="vuu3101",fontsize=16,color="green",shape="box"];629[label="vuu301",fontsize=16,color="green",shape="box"];630[label="vuu3101",fontsize=16,color="green",shape="box"];631[label="vuu301",fontsize=16,color="green",shape="box"];632[label="vuu3101",fontsize=16,color="green",shape="box"];633[label="vuu301",fontsize=16,color="green",shape="box"];634[label="vuu3101",fontsize=16,color="green",shape="box"];635[label="vuu301",fontsize=16,color="green",shape="box"];636[label="vuu3101",fontsize=16,color="green",shape="box"];637[label="vuu301",fontsize=16,color="green",shape="box"];638[label="vuu3101",fontsize=16,color="green",shape="box"];639[label="vuu302",fontsize=16,color="green",shape="box"];640[label="vuu3102",fontsize=16,color="green",shape="box"];641[label="vuu302",fontsize=16,color="green",shape="box"];642[label="vuu3102",fontsize=16,color="green",shape="box"];643[label="vuu302",fontsize=16,color="green",shape="box"];644[label="vuu3102",fontsize=16,color="green",shape="box"];645[label="vuu302",fontsize=16,color="green",shape="box"];646[label="vuu3102",fontsize=16,color="green",shape="box"];647[label="vuu302",fontsize=16,color="green",shape="box"];648[label="vuu3102",fontsize=16,color="green",shape="box"];649[label="vuu302",fontsize=16,color="green",shape="box"];650[label="vuu3102",fontsize=16,color="green",shape="box"];651[label="vuu302",fontsize=16,color="green",shape="box"];652[label="vuu3102",fontsize=16,color="green",shape="box"];653[label="vuu302",fontsize=16,color="green",shape="box"];654[label="vuu3102",fontsize=16,color="green",shape="box"];655[label="vuu302",fontsize=16,color="green",shape="box"];656[label="vuu3102",fontsize=16,color="green",shape="box"];657[label="vuu302",fontsize=16,color="green",shape="box"];658[label="vuu3102",fontsize=16,color="green",shape="box"];659[label="vuu302",fontsize=16,color="green",shape="box"];660[label="vuu3102",fontsize=16,color="green",shape="box"];661[label="vuu302",fontsize=16,color="green",shape="box"];662[label="vuu3102",fontsize=16,color="green",shape="box"];663[label="vuu302",fontsize=16,color="green",shape="box"];664[label="vuu3102",fontsize=16,color="green",shape="box"];665[label="vuu302",fontsize=16,color="green",shape="box"];666[label="vuu3102",fontsize=16,color="green",shape="box"];667[label="vuu3000",fontsize=16,color="green",shape="box"];668[label="vuu31000",fontsize=16,color="green",shape="box"];669[label="vuu3000",fontsize=16,color="green",shape="box"];670[label="vuu31000",fontsize=16,color="green",shape="box"];671 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vuu9) vuu110 vuu111 ((==) vuu9 vuu110))",fontsize=16,color="magenta"];685 -> 694[label="",style="dashed", color="magenta", weight=3]; 685 -> 695[label="",style="dashed", color="magenta", weight=3]; 685 -> 696[label="",style="dashed", color="magenta", weight=3]; 685 -> 697[label="",style="dashed", color="magenta", weight=3]; 686[label="span2Ys0 ((==) vuu9) [] ([],[])",fontsize=16,color="black",shape="box"];686 -> 698[label="",style="solid", color="black", weight=3]; 687 -> 699[label="",style="dashed", color="red", weight=0]; 687[label="span2Zs0 ((==) vuu18) (vuu200 : vuu201) (span2Span1 ((==) vuu18) vuu201 ((==) vuu18) vuu200 vuu201 ((==) vuu18 vuu200))",fontsize=16,color="magenta"];687 -> 700[label="",style="dashed", color="magenta", weight=3]; 687 -> 701[label="",style="dashed", color="magenta", weight=3]; 687 -> 702[label="",style="dashed", color="magenta", weight=3]; 687 -> 703[label="",style="dashed", color="magenta", weight=3]; 688[label="span2Zs0 ((==) vuu18) [] 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weight=9]; 1127 -> 713[label="",style="solid", color="blue", weight=3]; 1128[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];697 -> 1128[label="",style="solid", color="blue", weight=9]; 1128 -> 714[label="",style="solid", color="blue", weight=3]; 1129[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];697 -> 1129[label="",style="solid", color="blue", weight=9]; 1129 -> 715[label="",style="solid", color="blue", weight=3]; 1130[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];697 -> 1130[label="",style="solid", color="blue", weight=9]; 1130 -> 716[label="",style="solid", color="blue", weight=3]; 1131[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];697 -> 1131[label="",style="solid", color="blue", weight=9]; 1131 -> 717[label="",style="solid", color="blue", weight=3]; 1132[label="== :: (Either a b) -> (Either a b) 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weight=9]; 1136 -> 722[label="",style="solid", color="blue", weight=3]; 693[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (span2Span1 ((==) vuu33) vuu35 ((==) vuu33) vuu34 vuu35 vuu36)",fontsize=16,color="burlywood",shape="triangle"];1137[label="vuu36/False",fontsize=10,color="white",style="solid",shape="box"];693 -> 1137[label="",style="solid", color="burlywood", weight=9]; 1137 -> 723[label="",style="solid", color="burlywood", weight=3]; 1138[label="vuu36/True",fontsize=10,color="white",style="solid",shape="box"];693 -> 1138[label="",style="solid", color="burlywood", weight=9]; 1138 -> 724[label="",style="solid", color="burlywood", weight=3]; 698[label="[]",fontsize=16,color="green",shape="box"];700[label="vuu18",fontsize=16,color="green",shape="box"];701[label="vuu201",fontsize=16,color="green",shape="box"];702[label="(==) vuu18 vuu200",fontsize=16,color="blue",shape="box"];1139[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1139[label="",style="solid", color="blue", weight=9]; 1139 -> 725[label="",style="solid", color="blue", weight=3]; 1140[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1140[label="",style="solid", color="blue", weight=9]; 1140 -> 726[label="",style="solid", color="blue", weight=3]; 1141[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1141[label="",style="solid", color="blue", weight=9]; 1141 -> 727[label="",style="solid", color="blue", weight=3]; 1142[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1142[label="",style="solid", color="blue", weight=9]; 1142 -> 728[label="",style="solid", color="blue", weight=3]; 1143[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1143[label="",style="solid", color="blue", weight=9]; 1143 -> 729[label="",style="solid", color="blue", weight=3]; 1144[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1144[label="",style="solid", color="blue", weight=9]; 1144 -> 730[label="",style="solid", color="blue", weight=3]; 1145[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1145[label="",style="solid", color="blue", weight=9]; 1145 -> 731[label="",style="solid", color="blue", weight=3]; 1146[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1146[label="",style="solid", color="blue", weight=9]; 1146 -> 732[label="",style="solid", color="blue", weight=3]; 1147[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1147[label="",style="solid", color="blue", weight=9]; 1147 -> 733[label="",style="solid", color="blue", weight=3]; 1148[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1148[label="",style="solid", color="blue", weight=9]; 1148 -> 734[label="",style="solid", color="blue", weight=3]; 1149[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1149[label="",style="solid", color="blue", weight=9]; 1149 -> 735[label="",style="solid", color="blue", weight=3]; 1150[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1150[label="",style="solid", color="blue", weight=9]; 1150 -> 736[label="",style="solid", color="blue", weight=3]; 1151[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1151[label="",style="solid", color="blue", weight=9]; 1151 -> 737[label="",style="solid", color="blue", weight=3]; 1152[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];702 -> 1152[label="",style="solid", color="blue", weight=9]; 1152 -> 738[label="",style="solid", color="blue", weight=3]; 703[label="vuu200",fontsize=16,color="green",shape="box"];699[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (span2Span1 ((==) vuu42) vuu44 ((==) vuu42) vuu43 vuu44 vuu45)",fontsize=16,color="burlywood",shape="triangle"];1153[label="vuu45/False",fontsize=10,color="white",style="solid",shape="box"];699 -> 1153[label="",style="solid", color="burlywood", weight=9]; 1153 -> 739[label="",style="solid", color="burlywood", weight=3]; 1154[label="vuu45/True",fontsize=10,color="white",style="solid",shape="box"];699 -> 1154[label="",style="solid", color="burlywood", weight=9]; 1154 -> 740[label="",style="solid", color="burlywood", weight=3]; 704[label="[]",fontsize=16,color="green",shape="box"];705[label="primMulNat vuu3000 vuu31010",fontsize=16,color="burlywood",shape="triangle"];1155[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];705 -> 1155[label="",style="solid", color="burlywood", weight=9]; 1155 -> 741[label="",style="solid", color="burlywood", weight=3]; 1156[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];705 -> 1156[label="",style="solid", color="burlywood", weight=9]; 1156 -> 742[label="",style="solid", color="burlywood", weight=3]; 706 -> 705[label="",style="dashed", color="red", weight=0]; 706[label="primMulNat vuu3000 vuu31010",fontsize=16,color="magenta"];706 -> 743[label="",style="dashed", color="magenta", weight=3]; 707 -> 705[label="",style="dashed", color="red", weight=0]; 707[label="primMulNat vuu3000 vuu31010",fontsize=16,color="magenta"];707 -> 744[label="",style="dashed", color="magenta", weight=3]; 708 -> 705[label="",style="dashed", color="red", weight=0]; 708[label="primMulNat vuu3000 vuu31010",fontsize=16,color="magenta"];708 -> 745[label="",style="dashed", color="magenta", weight=3]; 708 -> 746[label="",style="dashed", color="magenta", weight=3]; 709 -> 34[label="",style="dashed", color="red", weight=0]; 709[label="(==) vuu9 vuu110",fontsize=16,color="magenta"];709 -> 747[label="",style="dashed", color="magenta", weight=3]; 709 -> 748[label="",style="dashed", color="magenta", weight=3]; 710 -> 35[label="",style="dashed", color="red", weight=0]; 710[label="(==) vuu9 vuu110",fontsize=16,color="magenta"];710 -> 749[label="",style="dashed", color="magenta", weight=3]; 710 -> 750[label="",style="dashed", color="magenta", weight=3]; 711 -> 36[label="",style="dashed", color="red", weight=0]; 711[label="(==) vuu9 vuu110",fontsize=16,color="magenta"];711 -> 751[label="",style="dashed", color="magenta", weight=3]; 711 -> 752[label="",style="dashed", color="magenta", weight=3]; 712 -> 37[label="",style="dashed", color="red", weight=0]; 712[label="(==) vuu9 vuu110",fontsize=16,color="magenta"];712 -> 753[label="",style="dashed", color="magenta", weight=3]; 712 -> 754[label="",style="dashed", color="magenta", weight=3]; 713 -> 38[label="",style="dashed", color="red", weight=0]; 713[label="(==) vuu9 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vuu110",fontsize=16,color="magenta"];721 -> 771[label="",style="dashed", color="magenta", weight=3]; 721 -> 772[label="",style="dashed", color="magenta", weight=3]; 722 -> 47[label="",style="dashed", color="red", weight=0]; 722[label="(==) vuu9 vuu110",fontsize=16,color="magenta"];722 -> 773[label="",style="dashed", color="magenta", weight=3]; 722 -> 774[label="",style="dashed", color="magenta", weight=3]; 723[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (span2Span1 ((==) vuu33) vuu35 ((==) vuu33) vuu34 vuu35 False)",fontsize=16,color="black",shape="box"];723 -> 775[label="",style="solid", color="black", weight=3]; 724[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (span2Span1 ((==) vuu33) vuu35 ((==) vuu33) vuu34 vuu35 True)",fontsize=16,color="black",shape="box"];724 -> 776[label="",style="solid", color="black", weight=3]; 725 -> 34[label="",style="dashed", color="red", weight=0]; 725[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];725 -> 777[label="",style="dashed", color="magenta", weight=3]; 725 -> 778[label="",style="dashed", color="magenta", weight=3]; 726 -> 35[label="",style="dashed", color="red", weight=0]; 726[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];726 -> 779[label="",style="dashed", color="magenta", weight=3]; 726 -> 780[label="",style="dashed", color="magenta", weight=3]; 727 -> 36[label="",style="dashed", color="red", weight=0]; 727[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];727 -> 781[label="",style="dashed", color="magenta", weight=3]; 727 -> 782[label="",style="dashed", color="magenta", weight=3]; 728 -> 37[label="",style="dashed", color="red", weight=0]; 728[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];728 -> 783[label="",style="dashed", color="magenta", weight=3]; 728 -> 784[label="",style="dashed", color="magenta", weight=3]; 729 -> 38[label="",style="dashed", color="red", weight=0]; 729[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];729 -> 785[label="",style="dashed", color="magenta", weight=3]; 729 -> 786[label="",style="dashed", color="magenta", weight=3]; 730 -> 39[label="",style="dashed", color="red", weight=0]; 730[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];730 -> 787[label="",style="dashed", color="magenta", weight=3]; 730 -> 788[label="",style="dashed", color="magenta", weight=3]; 731 -> 40[label="",style="dashed", color="red", weight=0]; 731[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];731 -> 789[label="",style="dashed", color="magenta", weight=3]; 731 -> 790[label="",style="dashed", color="magenta", weight=3]; 732 -> 41[label="",style="dashed", color="red", weight=0]; 732[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];732 -> 791[label="",style="dashed", color="magenta", weight=3]; 732 -> 792[label="",style="dashed", color="magenta", weight=3]; 733 -> 42[label="",style="dashed", color="red", weight=0]; 733[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];733 -> 793[label="",style="dashed", color="magenta", weight=3]; 733 -> 794[label="",style="dashed", color="magenta", weight=3]; 734 -> 43[label="",style="dashed", color="red", weight=0]; 734[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];734 -> 795[label="",style="dashed", color="magenta", weight=3]; 734 -> 796[label="",style="dashed", color="magenta", weight=3]; 735 -> 44[label="",style="dashed", color="red", weight=0]; 735[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];735 -> 797[label="",style="dashed", color="magenta", weight=3]; 735 -> 798[label="",style="dashed", color="magenta", weight=3]; 736 -> 45[label="",style="dashed", color="red", weight=0]; 736[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];736 -> 799[label="",style="dashed", color="magenta", weight=3]; 736 -> 800[label="",style="dashed", color="magenta", weight=3]; 737 -> 46[label="",style="dashed", color="red", weight=0]; 737[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];737 -> 801[label="",style="dashed", color="magenta", weight=3]; 737 -> 802[label="",style="dashed", color="magenta", weight=3]; 738 -> 47[label="",style="dashed", color="red", weight=0]; 738[label="(==) vuu18 vuu200",fontsize=16,color="magenta"];738 -> 803[label="",style="dashed", color="magenta", weight=3]; 738 -> 804[label="",style="dashed", color="magenta", weight=3]; 739[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (span2Span1 ((==) vuu42) vuu44 ((==) vuu42) vuu43 vuu44 False)",fontsize=16,color="black",shape="box"];739 -> 805[label="",style="solid", color="black", weight=3]; 740[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (span2Span1 ((==) vuu42) vuu44 ((==) vuu42) vuu43 vuu44 True)",fontsize=16,color="black",shape="box"];740 -> 806[label="",style="solid", color="black", weight=3]; 741[label="primMulNat (Succ vuu30000) vuu31010",fontsize=16,color="burlywood",shape="box"];1157[label="vuu31010/Succ vuu310100",fontsize=10,color="white",style="solid",shape="box"];741 -> 1157[label="",style="solid", color="burlywood", weight=9]; 1157 -> 807[label="",style="solid", color="burlywood", weight=3]; 1158[label="vuu31010/Zero",fontsize=10,color="white",style="solid",shape="box"];741 -> 1158[label="",style="solid", color="burlywood", weight=9]; 1158 -> 808[label="",style="solid", color="burlywood", weight=3]; 742[label="primMulNat Zero vuu31010",fontsize=16,color="burlywood",shape="box"];1159[label="vuu31010/Succ vuu310100",fontsize=10,color="white",style="solid",shape="box"];742 -> 1159[label="",style="solid", color="burlywood", weight=9]; 1159 -> 809[label="",style="solid", color="burlywood", weight=3]; 1160[label="vuu31010/Zero",fontsize=10,color="white",style="solid",shape="box"];742 -> 1160[label="",style="solid", color="burlywood", weight=9]; 1160 -> 810[label="",style="solid", color="burlywood", weight=3]; 743[label="vuu31010",fontsize=16,color="green",shape="box"];744[label="vuu3000",fontsize=16,color="green",shape="box"];745[label="vuu3000",fontsize=16,color="green",shape="box"];746[label="vuu31010",fontsize=16,color="green",shape="box"];747[label="vuu9",fontsize=16,color="green",shape="box"];748[label="vuu110",fontsize=16,color="green",shape="box"];749[label="vuu9",fontsize=16,color="green",shape="box"];750[label="vuu110",fontsize=16,color="green",shape="box"];751[label="vuu9",fontsize=16,color="green",shape="box"];752[label="vuu110",fontsize=16,color="green",shape="box"];753[label="vuu9",fontsize=16,color="green",shape="box"];754[label="vuu110",fontsize=16,color="green",shape="box"];755[label="vuu9",fontsize=16,color="green",shape="box"];756[label="vuu110",fontsize=16,color="green",shape="box"];757[label="vuu9",fontsize=16,color="green",shape="box"];758[label="vuu110",fontsize=16,color="green",shape="box"];759[label="vuu9",fontsize=16,color="green",shape="box"];760[label="vuu110",fontsize=16,color="green",shape="box"];761[label="vuu9",fontsize=16,color="green",shape="box"];762[label="vuu110",fontsize=16,color="green",shape="box"];763[label="vuu9",fontsize=16,color="green",shape="box"];764[label="vuu110",fontsize=16,color="green",shape="box"];765[label="vuu9",fontsize=16,color="green",shape="box"];766[label="vuu110",fontsize=16,color="green",shape="box"];767[label="vuu9",fontsize=16,color="green",shape="box"];768[label="vuu110",fontsize=16,color="green",shape="box"];769[label="vuu9",fontsize=16,color="green",shape="box"];770[label="vuu110",fontsize=16,color="green",shape="box"];771[label="vuu9",fontsize=16,color="green",shape="box"];772[label="vuu110",fontsize=16,color="green",shape="box"];773[label="vuu9",fontsize=16,color="green",shape="box"];774[label="vuu110",fontsize=16,color="green",shape="box"];775[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (span2Span0 ((==) vuu33) vuu35 ((==) vuu33) vuu34 vuu35 otherwise)",fontsize=16,color="black",shape="box"];775 -> 811[label="",style="solid", color="black", weight=3]; 776 -> 812[label="",style="dashed", color="red", weight=0]; 776[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (vuu34 : span2Ys ((==) vuu33) vuu35,span2Zs ((==) vuu33) vuu35)",fontsize=16,color="magenta"];776 -> 813[label="",style="dashed", color="magenta", weight=3]; 776 -> 814[label="",style="dashed", color="magenta", weight=3]; 777[label="vuu18",fontsize=16,color="green",shape="box"];778[label="vuu200",fontsize=16,color="green",shape="box"];779[label="vuu18",fontsize=16,color="green",shape="box"];780[label="vuu200",fontsize=16,color="green",shape="box"];781[label="vuu18",fontsize=16,color="green",shape="box"];782[label="vuu200",fontsize=16,color="green",shape="box"];783[label="vuu18",fontsize=16,color="green",shape="box"];784[label="vuu200",fontsize=16,color="green",shape="box"];785[label="vuu18",fontsize=16,color="green",shape="box"];786[label="vuu200",fontsize=16,color="green",shape="box"];787[label="vuu18",fontsize=16,color="green",shape="box"];788[label="vuu200",fontsize=16,color="green",shape="box"];789[label="vuu18",fontsize=16,color="green",shape="box"];790[label="vuu200",fontsize=16,color="green",shape="box"];791[label="vuu18",fontsize=16,color="green",shape="box"];792[label="vuu200",fontsize=16,color="green",shape="box"];793[label="vuu18",fontsize=16,color="green",shape="box"];794[label="vuu200",fontsize=16,color="green",shape="box"];795[label="vuu18",fontsize=16,color="green",shape="box"];796[label="vuu200",fontsize=16,color="green",shape="box"];797[label="vuu18",fontsize=16,color="green",shape="box"];798[label="vuu200",fontsize=16,color="green",shape="box"];799[label="vuu18",fontsize=16,color="green",shape="box"];800[label="vuu200",fontsize=16,color="green",shape="box"];801[label="vuu18",fontsize=16,color="green",shape="box"];802[label="vuu200",fontsize=16,color="green",shape="box"];803[label="vuu18",fontsize=16,color="green",shape="box"];804[label="vuu200",fontsize=16,color="green",shape="box"];805[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (span2Span0 ((==) vuu42) vuu44 ((==) vuu42) vuu43 vuu44 otherwise)",fontsize=16,color="black",shape="box"];805 -> 815[label="",style="solid", color="black", weight=3]; 806 -> 816[label="",style="dashed", color="red", weight=0]; 806[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (vuu43 : span2Ys ((==) vuu42) vuu44,span2Zs ((==) vuu42) vuu44)",fontsize=16,color="magenta"];806 -> 817[label="",style="dashed", color="magenta", weight=3]; 806 -> 818[label="",style="dashed", color="magenta", weight=3]; 807[label="primMulNat (Succ vuu30000) (Succ vuu310100)",fontsize=16,color="black",shape="box"];807 -> 819[label="",style="solid", color="black", weight=3]; 808[label="primMulNat (Succ vuu30000) Zero",fontsize=16,color="black",shape="box"];808 -> 820[label="",style="solid", color="black", weight=3]; 809[label="primMulNat Zero (Succ vuu310100)",fontsize=16,color="black",shape="box"];809 -> 821[label="",style="solid", color="black", weight=3]; 810[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];810 -> 822[label="",style="solid", color="black", weight=3]; 811[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (span2Span0 ((==) vuu33) vuu35 ((==) vuu33) vuu34 vuu35 True)",fontsize=16,color="black",shape="box"];811 -> 823[label="",style="solid", color="black", weight=3]; 813 -> 171[label="",style="dashed", color="red", weight=0]; 813[label="span2Ys ((==) vuu33) vuu35",fontsize=16,color="magenta"];813 -> 824[label="",style="dashed", color="magenta", weight=3]; 813 -> 825[label="",style="dashed", color="magenta", weight=3]; 814 -> 173[label="",style="dashed", color="red", weight=0]; 814[label="span2Zs ((==) vuu33) vuu35",fontsize=16,color="magenta"];814 -> 826[label="",style="dashed", color="magenta", weight=3]; 814 -> 827[label="",style="dashed", color="magenta", weight=3]; 812[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) (vuu34 : vuu47,vuu46)",fontsize=16,color="black",shape="triangle"];812 -> 828[label="",style="solid", color="black", weight=3]; 815[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (span2Span0 ((==) vuu42) vuu44 ((==) vuu42) vuu43 vuu44 True)",fontsize=16,color="black",shape="box"];815 -> 829[label="",style="solid", color="black", weight=3]; 817 -> 173[label="",style="dashed", color="red", weight=0]; 817[label="span2Zs ((==) vuu42) vuu44",fontsize=16,color="magenta"];817 -> 830[label="",style="dashed", color="magenta", weight=3]; 817 -> 831[label="",style="dashed", color="magenta", weight=3]; 818 -> 171[label="",style="dashed", color="red", weight=0]; 818[label="span2Ys ((==) vuu42) vuu44",fontsize=16,color="magenta"];818 -> 832[label="",style="dashed", color="magenta", weight=3]; 818 -> 833[label="",style="dashed", color="magenta", weight=3]; 816[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) (vuu43 : vuu49,vuu48)",fontsize=16,color="black",shape="triangle"];816 -> 834[label="",style="solid", color="black", weight=3]; 819 -> 835[label="",style="dashed", color="red", weight=0]; 819[label="primPlusNat (primMulNat vuu30000 (Succ vuu310100)) (Succ vuu310100)",fontsize=16,color="magenta"];819 -> 836[label="",style="dashed", color="magenta", weight=3]; 820[label="Zero",fontsize=16,color="green",shape="box"];821[label="Zero",fontsize=16,color="green",shape="box"];822[label="Zero",fontsize=16,color="green",shape="box"];823[label="span2Ys0 ((==) vuu33) (vuu34 : vuu35) ([],vuu34 : vuu35)",fontsize=16,color="black",shape="box"];823 -> 837[label="",style="solid", color="black", weight=3]; 824[label="vuu33",fontsize=16,color="green",shape="box"];825[label="vuu35",fontsize=16,color="green",shape="box"];826[label="vuu33",fontsize=16,color="green",shape="box"];827[label="vuu35",fontsize=16,color="green",shape="box"];828[label="vuu34 : vuu47",fontsize=16,color="green",shape="box"];829[label="span2Zs0 ((==) vuu42) (vuu43 : vuu44) ([],vuu43 : vuu44)",fontsize=16,color="black",shape="box"];829 -> 838[label="",style="solid", color="black", weight=3]; 830[label="vuu42",fontsize=16,color="green",shape="box"];831[label="vuu44",fontsize=16,color="green",shape="box"];832[label="vuu42",fontsize=16,color="green",shape="box"];833[label="vuu44",fontsize=16,color="green",shape="box"];834[label="vuu48",fontsize=16,color="green",shape="box"];836 -> 705[label="",style="dashed", color="red", weight=0]; 836[label="primMulNat vuu30000 (Succ vuu310100)",fontsize=16,color="magenta"];836 -> 839[label="",style="dashed", color="magenta", weight=3]; 836 -> 840[label="",style="dashed", color="magenta", weight=3]; 835[label="primPlusNat vuu50 (Succ vuu310100)",fontsize=16,color="burlywood",shape="triangle"];1161[label="vuu50/Succ vuu500",fontsize=10,color="white",style="solid",shape="box"];835 -> 1161[label="",style="solid", color="burlywood", weight=9]; 1161 -> 841[label="",style="solid", color="burlywood", weight=3]; 1162[label="vuu50/Zero",fontsize=10,color="white",style="solid",shape="box"];835 -> 1162[label="",style="solid", color="burlywood", weight=9]; 1162 -> 842[label="",style="solid", color="burlywood", weight=3]; 837[label="[]",fontsize=16,color="green",shape="box"];838[label="vuu43 : vuu44",fontsize=16,color="green",shape="box"];839[label="vuu30000",fontsize=16,color="green",shape="box"];840[label="Succ vuu310100",fontsize=16,color="green",shape="box"];841[label="primPlusNat (Succ vuu500) (Succ vuu310100)",fontsize=16,color="black",shape="box"];841 -> 843[label="",style="solid", color="black", weight=3]; 842[label="primPlusNat Zero (Succ vuu310100)",fontsize=16,color="black",shape="box"];842 -> 844[label="",style="solid", color="black", weight=3]; 843[label="Succ (Succ (primPlusNat vuu500 vuu310100))",fontsize=16,color="green",shape="box"];843 -> 845[label="",style="dashed", color="green", weight=3]; 844[label="Succ vuu310100",fontsize=16,color="green",shape="box"];845[label="primPlusNat vuu500 vuu310100",fontsize=16,color="burlywood",shape="triangle"];1163[label="vuu500/Succ vuu5000",fontsize=10,color="white",style="solid",shape="box"];845 -> 1163[label="",style="solid", color="burlywood", weight=9]; 1163 -> 846[label="",style="solid", color="burlywood", weight=3]; 1164[label="vuu500/Zero",fontsize=10,color="white",style="solid",shape="box"];845 -> 1164[label="",style="solid", color="burlywood", weight=9]; 1164 -> 847[label="",style="solid", color="burlywood", weight=3]; 846[label="primPlusNat (Succ vuu5000) vuu310100",fontsize=16,color="burlywood",shape="box"];1165[label="vuu310100/Succ vuu3101000",fontsize=10,color="white",style="solid",shape="box"];846 -> 1165[label="",style="solid", color="burlywood", weight=9]; 1165 -> 848[label="",style="solid", color="burlywood", weight=3]; 1166[label="vuu310100/Zero",fontsize=10,color="white",style="solid",shape="box"];846 -> 1166[label="",style="solid", color="burlywood", weight=9]; 1166 -> 849[label="",style="solid", color="burlywood", weight=3]; 847[label="primPlusNat Zero vuu310100",fontsize=16,color="burlywood",shape="box"];1167[label="vuu310100/Succ vuu3101000",fontsize=10,color="white",style="solid",shape="box"];847 -> 1167[label="",style="solid", color="burlywood", weight=9]; 1167 -> 850[label="",style="solid", color="burlywood", weight=3]; 1168[label="vuu310100/Zero",fontsize=10,color="white",style="solid",shape="box"];847 -> 1168[label="",style="solid", color="burlywood", weight=9]; 1168 -> 851[label="",style="solid", color="burlywood", weight=3]; 848[label="primPlusNat (Succ vuu5000) (Succ vuu3101000)",fontsize=16,color="black",shape="box"];848 -> 852[label="",style="solid", color="black", weight=3]; 849[label="primPlusNat (Succ vuu5000) Zero",fontsize=16,color="black",shape="box"];849 -> 853[label="",style="solid", color="black", weight=3]; 850[label="primPlusNat Zero (Succ vuu3101000)",fontsize=16,color="black",shape="box"];850 -> 854[label="",style="solid", color="black", weight=3]; 851[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];851 -> 855[label="",style="solid", color="black", weight=3]; 852[label="Succ (Succ (primPlusNat vuu5000 vuu3101000))",fontsize=16,color="green",shape="box"];852 -> 856[label="",style="dashed", color="green", weight=3]; 853[label="Succ vuu5000",fontsize=16,color="green",shape="box"];854[label="Succ vuu3101000",fontsize=16,color="green",shape="box"];855[label="Zero",fontsize=16,color="green",shape="box"];856 -> 845[label="",style="dashed", color="red", weight=0]; 856[label="primPlusNat vuu5000 vuu3101000",fontsize=16,color="magenta"];856 -> 857[label="",style="dashed", color="magenta", weight=3]; 856 -> 858[label="",style="dashed", color="magenta", weight=3]; 857[label="vuu5000",fontsize=16,color="green",shape="box"];858[label="vuu3101000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs3(Just(vuu300), Just(vuu3100), app(app(ty_Either, bdg), bdh)) -> new_esEs1(vuu300, vuu3100, bdg, bdh) new_esEs1(Left(vuu300), Left(vuu3100), app(app(ty_Either, gh), ha), gd) -> new_esEs1(vuu300, vuu3100, gh, ha) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(ty_@2, bg), bh)) -> new_esEs2(vuu300, vuu3100, bg, bh) new_esEs1(Right(vuu300), Right(vuu3100), he, app(ty_Maybe, baf)) -> new_esEs3(vuu300, vuu3100, baf) new_esEs3(Just(vuu300), Just(vuu3100), app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(vuu300, vuu3100, bdd, bde, bdf) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(app(ty_@3, ea), eb), ec), ce) -> new_esEs0(vuu301, vuu3101, ea, eb, ec) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(ty_Maybe, eh), ce) -> new_esEs3(vuu301, vuu3101, eh) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(ty_Maybe, bdb)) -> new_esEs3(vuu301, vuu3101, bdb) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(ty_@2, bch), bda)) -> new_esEs2(vuu301, vuu3101, bch, bda) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(ty_[], bcb)) -> new_esEs(vuu301, vuu3101, bcb) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), cb) -> new_esEs(vuu301, vuu3101, cb) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(ty_Maybe, gb)) -> new_esEs3(vuu302, vuu3102, gb) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(ty_Maybe, bbh), bah) -> new_esEs3(vuu300, vuu3100, bbh) new_esEs3(Just(vuu300), Just(vuu3100), app(ty_Maybe, bec)) -> new_esEs3(vuu300, vuu3100, bec) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(ty_Either, db), dc), cd, ce) -> new_esEs1(vuu300, vuu3100, db, dc) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(ty_@2, fh), ga)) -> new_esEs2(vuu302, vuu3102, fh, ga) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(ty_[], ba)) -> new_esEs(vuu300, vuu3100, ba) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(ty_Maybe, df), cd, ce) -> new_esEs3(vuu300, vuu3100, df) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(ty_@2, ef), eg), ce) -> new_esEs2(vuu301, vuu3101, ef, eg) new_esEs1(Left(vuu300), Left(vuu3100), app(ty_Maybe, hd), gd) -> new_esEs3(vuu300, vuu3100, hd) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(ty_@2, bbf), bbg), bah) -> new_esEs2(vuu300, vuu3100, bbf, bbg) new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(ty_@2, bad), bae)) -> new_esEs2(vuu300, vuu3100, bad, bae) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(vuu300, vuu3100, bb, bc, bd) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(app(ty_@3, fb), fc), fd)) -> new_esEs0(vuu302, vuu3102, fb, fc, fd) new_esEs1(Left(vuu300), Left(vuu3100), app(ty_[], gc), gd) -> new_esEs(vuu300, vuu3100, gc) new_esEs1(Left(vuu300), Left(vuu3100), app(app(app(ty_@3, ge), gf), gg), gd) -> new_esEs0(vuu300, vuu3100, ge, gf, gg) new_esEs3(Just(vuu300), Just(vuu3100), app(app(ty_@2, bea), beb)) -> new_esEs2(vuu300, vuu3100, bea, beb) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(ty_Either, be), bf)) -> new_esEs1(vuu300, vuu3100, be, bf) new_esEs3(Just(vuu300), Just(vuu3100), app(ty_[], bdc)) -> new_esEs(vuu300, vuu3100, bdc) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(ty_[], cc), cd, ce) -> new_esEs(vuu300, vuu3100, cc) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(ty_[], dh), ce) -> new_esEs(vuu301, vuu3101, dh) new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(ty_Maybe, ca)) -> new_esEs3(vuu300, vuu3100, ca) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(ty_[], fa)) -> new_esEs(vuu302, vuu3102, fa) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(ty_Either, ed), ee), ce) -> new_esEs1(vuu301, vuu3101, ed, ee) new_esEs1(Left(vuu300), Left(vuu3100), app(app(ty_@2, hb), hc), gd) -> new_esEs2(vuu300, vuu3100, hb, hc) new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(vuu300, vuu3100, hg, hh, baa) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(ty_[], bag), bah) -> new_esEs(vuu300, vuu3100, bag) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(ty_@2, dd), de), cd, ce) -> new_esEs2(vuu300, vuu3100, dd, de) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(app(ty_@3, bba), bbb), bbc), bah) -> new_esEs0(vuu300, vuu3100, bba, bbb, bbc) new_esEs1(Right(vuu300), Right(vuu3100), he, app(ty_[], hf)) -> new_esEs(vuu300, vuu3100, hf) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(ty_Either, bbd), bbe), bah) -> new_esEs1(vuu300, vuu3100, bbd, bbe) new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(ty_Either, bab), bac)) -> new_esEs1(vuu300, vuu3100, bab, bac) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(ty_Either, bcf), bcg)) -> new_esEs1(vuu301, vuu3101, bcf, bcg) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(app(ty_@3, cf), cg), da), cd, ce) -> new_esEs0(vuu300, vuu3100, cf, cg, da) new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(ty_Either, ff), fg)) -> new_esEs1(vuu302, vuu3102, ff, fg) new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(vuu301, vuu3101, bcc, bcd, bce) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_esEs3(Just(vuu300), Just(vuu3100), app(ty_Maybe, bec)) -> new_esEs3(vuu300, vuu3100, bec) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Just(vuu300), Just(vuu3100), app(app(ty_Either, bdg), bdh)) -> new_esEs1(vuu300, vuu3100, bdg, bdh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Just(vuu300), Just(vuu3100), app(ty_[], bdc)) -> new_esEs(vuu300, vuu3100, bdc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(ty_Maybe, ca)) -> new_esEs3(vuu300, vuu3100, ca) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(ty_Either, be), bf)) -> new_esEs1(vuu300, vuu3100, be, bf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Just(vuu300), Just(vuu3100), app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(vuu300, vuu3100, bdd, bde, bdf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Just(vuu300), Just(vuu3100), app(app(ty_@2, bea), beb)) -> new_esEs2(vuu300, vuu3100, bea, beb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(vuu300, vuu3100, bb, bc, bd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(app(ty_@2, bg), bh)) -> new_esEs2(vuu300, vuu3100, bg, bh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(Right(vuu300), Right(vuu3100), he, app(ty_Maybe, baf)) -> new_esEs3(vuu300, vuu3100, baf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(Left(vuu300), Left(vuu3100), app(ty_Maybe, hd), gd) -> new_esEs3(vuu300, vuu3100, hd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(Left(vuu300), Left(vuu3100), app(app(ty_Either, gh), ha), gd) -> new_esEs1(vuu300, vuu3100, gh, ha) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(ty_Either, bab), bac)) -> new_esEs1(vuu300, vuu3100, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(Left(vuu300), Left(vuu3100), app(ty_[], gc), gd) -> new_esEs(vuu300, vuu3100, gc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(Right(vuu300), Right(vuu3100), he, app(ty_[], hf)) -> new_esEs(vuu300, vuu3100, hf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(Left(vuu300), Left(vuu3100), app(app(app(ty_@3, ge), gf), gg), gd) -> new_esEs0(vuu300, vuu3100, ge, gf, gg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(vuu300, vuu3100, hg, hh, baa) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs1(Right(vuu300), Right(vuu3100), he, app(app(ty_@2, bad), bae)) -> new_esEs2(vuu300, vuu3100, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(Left(vuu300), Left(vuu3100), app(app(ty_@2, hb), hc), gd) -> new_esEs2(vuu300, vuu3100, hb, hc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(ty_Maybe, bdb)) -> new_esEs3(vuu301, vuu3101, bdb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(ty_Maybe, bbh), bah) -> new_esEs3(vuu300, vuu3100, bbh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(ty_Maybe, eh), ce) -> new_esEs3(vuu301, vuu3101, eh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(ty_Maybe, gb)) -> new_esEs3(vuu302, vuu3102, gb) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(ty_Maybe, df), cd, ce) -> new_esEs3(vuu300, vuu3100, df) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(ty_Either, bbd), bbe), bah) -> new_esEs1(vuu300, vuu3100, bbd, bbe) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(ty_Either, bcf), bcg)) -> new_esEs1(vuu301, vuu3101, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(ty_Either, db), dc), cd, ce) -> new_esEs1(vuu300, vuu3100, db, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(ty_Either, ed), ee), ce) -> new_esEs1(vuu301, vuu3101, ed, ee) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(ty_Either, ff), fg)) -> new_esEs1(vuu302, vuu3102, ff, fg) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(ty_[], bcb)) -> new_esEs(vuu301, vuu3101, bcb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(ty_[], bag), bah) -> new_esEs(vuu300, vuu3100, bag) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(app(ty_@3, bba), bbb), bbc), bah) -> new_esEs0(vuu300, vuu3100, bba, bbb, bbc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(vuu301, vuu3101, bcc, bcd, bce) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), bca, app(app(ty_@2, bch), bda)) -> new_esEs2(vuu301, vuu3101, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(@2(vuu300, vuu301), @2(vuu3100, vuu3101), app(app(ty_@2, bbf), bbg), bah) -> new_esEs2(vuu300, vuu3100, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(ty_[], cc), cd, ce) -> new_esEs(vuu300, vuu3100, cc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(ty_[], dh), ce) -> new_esEs(vuu301, vuu3101, dh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(ty_[], fa)) -> new_esEs(vuu302, vuu3102, fa) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), cb) -> new_esEs(vuu301, vuu3101, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs(:(vuu300, vuu301), :(vuu3100, vuu3101), app(ty_[], ba)) -> new_esEs(vuu300, vuu3100, ba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(app(ty_@3, ea), eb), ec), ce) -> new_esEs0(vuu301, vuu3101, ea, eb, ec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(app(ty_@3, fb), fc), fd)) -> new_esEs0(vuu302, vuu3102, fb, fc, fd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(app(ty_@3, cf), cg), da), cd, ce) -> new_esEs0(vuu300, vuu3100, cf, cg, da) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, cd, app(app(ty_@2, fh), ga)) -> new_esEs2(vuu302, vuu3102, fh, ga) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), dg, app(app(ty_@2, ef), eg), ce) -> new_esEs2(vuu301, vuu3101, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), app(app(ty_@2, dd), de), cd, ce) -> new_esEs2(vuu300, vuu3100, dd, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_groupBy(:(vuu30, vuu31), ba) -> new_groupBy(new_groupByZs1(vuu30, vuu31, ba), ba) The TRS R consists of the following rules: new_esEs12(vuu301, vuu3101, app(ty_Maybe, ea)) -> new_esEs22(vuu301, vuu3101, ea) new_esEs11(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs4(vuu9, vuu110, ty_Ordering) -> new_esEs17(vuu9, vuu110) new_esEs7(Double(vuu300, vuu301), Double(vuu3100, vuu3101)) -> new_esEs8(new_sr(vuu300, vuu3101), new_sr(vuu301, vuu3100)) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_span2Ys1(vuu9, [], ff) -> [] new_esEs5(vuu18, vuu200, ty_Bool) -> new_esEs9(vuu18, vuu200) new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(Just(vuu300), Just(vuu3100), ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), app(app(ty_@2, bga), bgb), bfa) -> new_esEs21(vuu300, vuu3100, bga, bgb) new_esEs12(vuu301, vuu3101, app(ty_[], cg)) -> new_esEs16(vuu301, vuu3101, cg) new_esEs22(Just(vuu300), Just(vuu3100), app(app(ty_Either, beb), bec)) -> new_esEs19(vuu300, vuu3100, beb, bec) new_esEs28(vuu30, vuu310, ty_Integer) -> new_esEs6(vuu30, vuu310) new_esEs19(Left(vuu300), Left(vuu3100), app(app(ty_Either, bfg), bfh), bfa) -> new_esEs19(vuu300, vuu3100, bfg, bfh) new_esEs11(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs27(vuu300, vuu3100, app(ty_[], bca)) -> new_esEs16(vuu300, vuu3100, bca) new_esEs26(vuu301, vuu3101, ty_Bool) -> new_esEs9(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Float, bfa) -> new_esEs15(vuu300, vuu3100) new_esEs28(vuu30, vuu310, ty_@0) -> new_esEs14(vuu30, vuu310) new_esEs22(Just(vuu300), Just(vuu3100), ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs28(vuu30, vuu310, ty_Char) -> new_esEs20(vuu30, vuu310) new_esEs20(Char(vuu300), Char(vuu3100)) -> new_primEqNat0(vuu300, vuu3100) new_esEs9(False, False) -> True new_esEs27(vuu300, vuu3100, app(ty_Maybe, bdb)) -> new_esEs22(vuu300, vuu3100, bdb) new_primMulNat0(Succ(vuu30000), Succ(vuu310100)) -> new_primPlusNat1(new_primMulNat0(vuu30000, Succ(vuu310100)), vuu310100) new_esEs11(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Char) -> new_esEs20(vuu18, vuu200) new_asAs(True, vuu27) -> vuu27 new_esEs22(Just(vuu300), Just(vuu3100), app(ty_[], bde)) -> new_esEs16(vuu300, vuu3100, bde) new_esEs26(vuu301, vuu3101, app(app(ty_@2, bbd), bbe)) -> new_esEs21(vuu301, vuu3101, bbd, bbe) new_esEs22(Just(vuu300), Just(vuu3100), app(app(ty_@2, bed), bee)) -> new_esEs21(vuu300, vuu3100, bed, bee) new_esEs28(vuu30, vuu310, ty_Bool) -> new_esEs9(vuu30, vuu310) new_primEqInt(Pos(Succ(vuu3000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu31000))) -> False new_esEs5(vuu18, vuu200, app(app(ty_@2, cae), caf)) -> new_esEs21(vuu18, vuu200, cae, caf) new_esEs17(LT, LT) -> True new_groupByZs1(vuu30, :(vuu310, vuu311), ba) -> new_groupByZs10(vuu30, vuu310, vuu311, new_esEs28(vuu30, vuu310, ba), ba) new_esEs6(Integer(vuu300), Integer(vuu3100)) -> new_primEqInt(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(ty_Maybe, bad)) -> new_esEs22(vuu300, vuu3100, bad) new_esEs19(Left(vuu300), Left(vuu3100), app(app(app(ty_@3, bfc), bfd), bfe), bfa) -> new_esEs10(vuu300, vuu3100, bfc, bfd, bfe) new_esEs26(vuu301, vuu3101, ty_Char) -> new_esEs20(vuu301, vuu3101) new_esEs27(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Double) -> new_esEs7(vuu18, vuu200) new_span2Zs1(vuu18, [], bdc) -> [] new_primEqNat0(Succ(vuu3000), Succ(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs13(vuu302, vuu3102, ty_Integer) -> new_esEs6(vuu302, vuu3102) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, ty_Double) -> new_esEs7(vuu301, vuu3101) new_esEs12(vuu301, vuu3101, app(app(ty_@2, dg), dh)) -> new_esEs21(vuu301, vuu3101, dg, dh) new_esEs4(vuu9, vuu110, ty_Float) -> new_esEs15(vuu9, vuu110) new_esEs4(vuu9, vuu110, app(app(app(ty_@3, fh), ga), gb)) -> new_esEs10(vuu9, vuu110, fh, ga, gb) new_esEs25(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(app(app(ty_@3, hd), he), hf)) -> new_esEs10(vuu300, vuu3100, hd, he, hf) new_esEs24(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs13(vuu302, vuu3102, ty_@0) -> new_esEs14(vuu302, vuu3102) new_esEs13(vuu302, vuu3102, ty_Ordering) -> new_esEs17(vuu302, vuu3102) new_esEs4(vuu9, vuu110, app(ty_Maybe, gh)) -> new_esEs22(vuu9, vuu110, gh) new_esEs9(True, True) -> True new_esEs28(vuu30, vuu310, ty_Float) -> new_esEs15(vuu30, vuu310) new_esEs11(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs16(:(vuu300, vuu301), :(vuu3100, vuu3101), bbh) -> new_asAs(new_esEs27(vuu300, vuu3100, bbh), new_esEs16(vuu301, vuu3101, bbh)) new_groupByZs10(vuu18, vuu19, vuu20, False, bdc) -> :(vuu19, vuu20) new_primMulNat0(Zero, Zero) -> Zero new_esEs11(vuu300, vuu3100, app(app(ty_@2, cd), ce)) -> new_esEs21(vuu300, vuu3100, cd, ce) new_esEs27(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs22(Nothing, Just(vuu3100), bdd) -> False new_esEs22(Just(vuu300), Nothing, bdd) -> False new_esEs22(Nothing, Nothing, bdd) -> True new_esEs21(@2(vuu300, vuu301), @2(vuu3100, vuu3101), ha, hb) -> new_asAs(new_esEs25(vuu300, vuu3100, ha), new_esEs26(vuu301, vuu3101, hb)) new_esEs12(vuu301, vuu3101, ty_Float) -> new_esEs15(vuu301, vuu3101) new_span2Zs00(vuu42, vuu43, vuu44, vuu49, vuu48, fd) -> vuu48 new_esEs22(Just(vuu300), Just(vuu3100), ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs28(vuu30, vuu310, app(app(ty_@2, ha), hb)) -> new_esEs21(vuu30, vuu310, ha, hb) new_esEs11(vuu300, vuu3100, app(ty_Ratio, ca)) -> new_esEs18(vuu300, vuu3100, ca) new_esEs12(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs25(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_primEqNat0(Succ(vuu3000), Zero) -> False new_primEqNat0(Zero, Succ(vuu31000)) -> False new_esEs27(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs14(@0, @0) -> True new_esEs27(vuu300, vuu3100, app(ty_Ratio, bce)) -> new_esEs18(vuu300, vuu3100, bce) new_span2Zs01(vuu42, vuu43, vuu44, True, fd) -> new_span2Zs00(vuu42, vuu43, vuu44, new_span2Ys1(vuu42, vuu44, fd), new_span2Zs1(vuu42, vuu44, fd), fd) new_esEs28(vuu30, vuu310, app(ty_Ratio, beg)) -> new_esEs18(vuu30, vuu310, beg) new_esEs27(vuu300, vuu3100, app(app(app(ty_@3, bcb), bcc), bcd)) -> new_esEs10(vuu300, vuu3100, bcb, bcc, bcd) new_esEs13(vuu302, vuu3102, ty_Float) -> new_esEs15(vuu302, vuu3102) new_esEs27(vuu300, vuu3100, app(app(ty_@2, bch), bda)) -> new_esEs21(vuu300, vuu3100, bch, bda) new_esEs19(Left(vuu300), Left(vuu3100), ty_@0, bfa) -> new_esEs14(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, app(app(ty_Either, de), df)) -> new_esEs19(vuu301, vuu3101, de, df) new_esEs26(vuu301, vuu3101, app(ty_Maybe, bbf)) -> new_esEs22(vuu301, vuu3101, bbf) new_esEs22(Just(vuu300), Just(vuu3100), app(ty_Maybe, bef)) -> new_esEs22(vuu300, vuu3100, bef) new_esEs17(EQ, GT) -> False new_esEs17(GT, EQ) -> False new_esEs28(vuu30, vuu310, ty_Double) -> new_esEs7(vuu30, vuu310) new_groupByZs10(vuu18, vuu19, vuu20, True, bdc) -> new_span2Zs1(vuu18, vuu20, bdc) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs4(vuu9, vuu110, app(ty_Ratio, gc)) -> new_esEs18(vuu9, vuu110, gc) new_esEs25(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Int) -> new_esEs8(vuu18, vuu200) new_esEs22(Just(vuu300), Just(vuu3100), ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, ty_Char) -> new_esEs20(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, ty_Ordering) -> new_esEs17(vuu301, vuu3101) new_esEs17(GT, GT) -> True new_primEqInt(Neg(Succ(vuu3000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu31000))) -> False new_esEs26(vuu301, vuu3101, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs10(vuu301, vuu3101, baf, bag, bah) new_esEs26(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_primEqInt(Pos(Succ(vuu3000)), Pos(Succ(vuu31000))) -> new_primEqNat0(vuu3000, vuu31000) new_esEs11(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Float) -> new_esEs15(vuu18, vuu200) new_esEs22(Just(vuu300), Just(vuu3100), ty_Integer) -> new_esEs6(vuu300, vuu3100) new_span2Zs1(vuu18, :(vuu200, vuu201), bdc) -> new_span2Zs01(vuu18, vuu200, vuu201, new_esEs5(vuu18, vuu200, bdc), bdc) new_span2Ys1(vuu9, :(vuu110, vuu111), ff) -> new_span2Ys00(vuu9, vuu110, vuu111, new_esEs4(vuu9, vuu110, ff), ff) new_sr(Pos(vuu3000), Neg(vuu31010)) -> Neg(new_primMulNat0(vuu3000, vuu31010)) new_sr(Neg(vuu3000), Pos(vuu31010)) -> Neg(new_primMulNat0(vuu3000, vuu31010)) new_esEs5(vuu18, vuu200, app(app(ty_Either, cac), cad)) -> new_esEs19(vuu18, vuu200, cac, cad) new_esEs22(Just(vuu300), Just(vuu3100), ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs28(vuu30, vuu310, ty_Int) -> new_esEs8(vuu30, vuu310) new_esEs26(vuu301, vuu3101, ty_@0) -> new_esEs14(vuu301, vuu3101) new_primEqInt(Pos(Succ(vuu3000)), Neg(vuu3100)) -> False new_primEqInt(Neg(Succ(vuu3000)), Pos(vuu3100)) -> False new_esEs4(vuu9, vuu110, ty_Double) -> new_esEs7(vuu9, vuu110) new_esEs4(vuu9, vuu110, app(app(ty_@2, gf), gg)) -> new_esEs21(vuu9, vuu110, gf, gg) new_esEs19(Left(vuu300), Left(vuu3100), ty_Ordering, bfa) -> new_esEs17(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(ty_[], hc)) -> new_esEs16(vuu300, vuu3100, hc) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(ty_[], bgd)) -> new_esEs16(vuu300, vuu3100, bgd) new_esEs27(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), ty_Integer, bfa) -> new_esEs6(vuu300, vuu3100) new_esEs28(vuu30, vuu310, app(ty_[], bbh)) -> new_esEs16(vuu30, vuu310, bbh) new_esEs25(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs8(vuu30, vuu310) -> new_primEqInt(vuu30, vuu310) new_esEs27(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs22(Just(vuu300), Just(vuu3100), app(ty_Ratio, bea)) -> new_esEs18(vuu300, vuu3100, bea) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(app(ty_Either, bha), bhb)) -> new_esEs19(vuu300, vuu3100, bha, bhb) new_esEs12(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_esEs18(:%(vuu300, vuu301), :%(vuu3100, vuu3101), beg) -> new_asAs(new_esEs23(vuu300, vuu3100, beg), new_esEs24(vuu301, vuu3101, beg)) new_esEs13(vuu302, vuu3102, ty_Double) -> new_esEs7(vuu302, vuu3102) new_esEs23(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs28(vuu30, vuu310, app(ty_Maybe, bdd)) -> new_esEs22(vuu30, vuu310, bdd) new_esEs27(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_Maybe, bgc), bfa) -> new_esEs22(vuu300, vuu3100, bgc) new_sr(Neg(vuu3000), Neg(vuu31010)) -> Pos(new_primMulNat0(vuu3000, vuu31010)) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_[], bfb), bfa) -> new_esEs16(vuu300, vuu3100, bfb) new_esEs4(vuu9, vuu110, ty_Int) -> new_esEs8(vuu9, vuu110) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, app(ty_[], eb)) -> new_esEs16(vuu302, vuu3102, eb) new_esEs4(vuu9, vuu110, ty_Bool) -> new_esEs9(vuu9, vuu110) new_esEs13(vuu302, vuu3102, app(ty_Maybe, fc)) -> new_esEs22(vuu302, vuu3102, fc) new_esEs22(Just(vuu300), Just(vuu3100), app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs10(vuu300, vuu3100, bdf, bdg, bdh) new_esEs25(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_primEqInt(Pos(Zero), Neg(Succ(vuu31000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu31000))) -> False new_primPlusNat0(Succ(vuu5000), Succ(vuu3101000)) -> Succ(Succ(new_primPlusNat0(vuu5000, vuu3101000))) new_span2Ys01(vuu33, vuu34, vuu35, vuu47, vuu46, bbg) -> :(vuu34, vuu47) new_esEs12(vuu301, vuu3101, app(ty_Ratio, dd)) -> new_esEs18(vuu301, vuu3101, dd) new_esEs13(vuu302, vuu3102, ty_Int) -> new_esEs8(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, app(ty_[], bae)) -> new_esEs16(vuu301, vuu3101, bae) new_esEs17(EQ, EQ) -> True new_span2Ys00(vuu33, vuu34, vuu35, True, bbg) -> new_span2Ys01(vuu33, vuu34, vuu35, new_span2Ys1(vuu33, vuu35, bbg), new_span2Zs1(vuu33, vuu35, bbg), bbg) new_esEs4(vuu9, vuu110, app(app(ty_Either, gd), ge)) -> new_esEs19(vuu9, vuu110, gd, ge) new_primEqInt(Neg(Succ(vuu3000)), Neg(Succ(vuu31000))) -> new_primEqNat0(vuu3000, vuu31000) new_esEs17(LT, EQ) -> False new_esEs17(EQ, LT) -> False new_esEs28(vuu30, vuu310, app(app(ty_Either, beh), bfa)) -> new_esEs19(vuu30, vuu310, beh, bfa) new_esEs19(Left(vuu300), Left(vuu3100), ty_Char, bfa) -> new_esEs20(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, app(app(ty_Either, eg), eh)) -> new_esEs19(vuu302, vuu3102, eg, eh) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(app(ty_@2, bhc), bhd)) -> new_esEs21(vuu300, vuu3100, bhc, bhd) new_esEs12(vuu301, vuu3101, ty_Char) -> new_esEs20(vuu301, vuu3101) new_esEs25(vuu300, vuu3100, app(app(ty_Either, hh), baa)) -> new_esEs19(vuu300, vuu3100, hh, baa) new_esEs11(vuu300, vuu3100, app(app(ty_Either, cb), cc)) -> new_esEs19(vuu300, vuu3100, cb, cc) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, app(ty_Maybe, cf)) -> new_esEs22(vuu300, vuu3100, cf) new_primMulNat0(Succ(vuu30000), Zero) -> Zero new_primMulNat0(Zero, Succ(vuu310100)) -> Zero new_sr(Pos(vuu3000), Pos(vuu31010)) -> Pos(new_primMulNat0(vuu3000, vuu31010)) new_esEs19(Left(vuu300), Left(vuu3100), ty_Bool, bfa) -> new_esEs9(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(ty_Maybe, bhe)) -> new_esEs22(vuu300, vuu3100, bhe) new_esEs11(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs5(vuu18, vuu200, app(ty_Ratio, cab)) -> new_esEs18(vuu18, vuu200, cab) new_primPlusNat1(Succ(vuu500), vuu310100) -> Succ(Succ(new_primPlusNat0(vuu500, vuu310100))) new_esEs27(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs17(LT, GT) -> False new_esEs17(GT, LT) -> False new_esEs22(Just(vuu300), Just(vuu3100), ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs24(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_esEs12(vuu301, vuu3101, ty_Ordering) -> new_esEs17(vuu301, vuu3101) new_primPlusNat0(Succ(vuu5000), Zero) -> Succ(vuu5000) new_primPlusNat0(Zero, Succ(vuu3101000)) -> Succ(vuu3101000) new_esEs11(vuu300, vuu3100, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs10(vuu300, vuu3100, bf, bg, bh) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(vuu301, vuu3101, app(ty_Ratio, bba)) -> new_esEs18(vuu301, vuu3101, bba) new_esEs13(vuu302, vuu3102, ty_Bool) -> new_esEs9(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, app(app(ty_Either, bbb), bbc)) -> new_esEs19(vuu301, vuu3101, bbb, bbc) new_esEs28(vuu30, vuu310, app(app(app(ty_@3, bb), bc), bd)) -> new_esEs10(vuu30, vuu310, bb, bc, bd) new_primPlusNat1(Zero, vuu310100) -> Succ(vuu310100) new_span2Zs01(vuu42, vuu43, vuu44, False, fd) -> :(vuu43, vuu44) new_esEs28(vuu30, vuu310, ty_Ordering) -> new_esEs17(vuu30, vuu310) new_esEs26(vuu301, vuu3101, ty_Double) -> new_esEs7(vuu301, vuu3101) new_esEs5(vuu18, vuu200, ty_Integer) -> new_esEs6(vuu18, vuu200) new_esEs10(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), bb, bc, bd) -> new_asAs(new_esEs11(vuu300, vuu3100, bb), new_asAs(new_esEs12(vuu301, vuu3101, bc), new_esEs13(vuu302, vuu3102, bd))) new_esEs12(vuu301, vuu3101, app(app(app(ty_@3, da), db), dc)) -> new_esEs10(vuu301, vuu3101, da, db, dc) new_esEs5(vuu18, vuu200, app(ty_Maybe, cag)) -> new_esEs22(vuu18, vuu200, cag) new_esEs12(vuu301, vuu3101, ty_Bool) -> new_esEs9(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Double, bfa) -> new_esEs7(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs4(vuu9, vuu110, ty_Char) -> new_esEs20(vuu9, vuu110) new_esEs26(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs5(vuu18, vuu200, app(ty_[], bhf)) -> new_esEs16(vuu18, vuu200, bhf) new_groupByZs1(vuu30, [], ba) -> [] new_esEs27(vuu300, vuu3100, app(app(ty_Either, bcf), bcg)) -> new_esEs19(vuu300, vuu3100, bcf, bcg) new_esEs13(vuu302, vuu3102, app(app(ty_@2, fa), fb)) -> new_esEs21(vuu302, vuu3102, fa, fb) new_esEs16(:(vuu300, vuu301), [], bbh) -> False new_esEs16([], :(vuu3100, vuu3101), bbh) -> False new_esEs13(vuu302, vuu3102, app(app(app(ty_@3, ec), ed), ee)) -> new_esEs10(vuu302, vuu3102, ec, ed, ee) new_span2Ys00(vuu33, vuu34, vuu35, False, bbg) -> [] new_esEs4(vuu9, vuu110, ty_@0) -> new_esEs14(vuu9, vuu110) new_esEs27(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(vuu9, vuu110, ty_Integer) -> new_esEs6(vuu9, vuu110) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_Ratio, bff), bfa) -> new_esEs18(vuu300, vuu3100, bff) new_primEqNat0(Zero, Zero) -> True new_esEs16([], [], bbh) -> True new_esEs25(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_@0) -> new_esEs14(vuu18, vuu200) new_esEs9(False, True) -> False new_esEs9(True, False) -> False new_esEs22(Just(vuu300), Just(vuu3100), ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, ty_@0) -> new_esEs14(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Int, bfa) -> new_esEs8(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(ty_Ratio, bgh)) -> new_esEs18(vuu300, vuu3100, bgh) new_esEs26(vuu301, vuu3101, ty_Float) -> new_esEs15(vuu301, vuu3101) new_esEs5(vuu18, vuu200, app(app(app(ty_@3, bhg), bhh), caa)) -> new_esEs10(vuu18, vuu200, bhg, bhh, caa) new_esEs13(vuu302, vuu3102, app(ty_Ratio, ef)) -> new_esEs18(vuu302, vuu3102, ef) new_asAs(False, vuu27) -> False new_esEs19(Left(vuu300), Right(vuu3100), beh, bfa) -> False new_esEs19(Right(vuu300), Left(vuu3100), beh, bfa) -> False new_esEs25(vuu300, vuu3100, app(ty_Ratio, hg)) -> new_esEs18(vuu300, vuu3100, hg) new_esEs23(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Ordering) -> new_esEs17(vuu18, vuu200) new_esEs25(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(app(ty_@2, bab), bac)) -> new_esEs21(vuu300, vuu3100, bab, bac) new_esEs11(vuu300, vuu3100, app(ty_[], be)) -> new_esEs16(vuu300, vuu3100, be) new_esEs4(vuu9, vuu110, app(ty_[], fg)) -> new_esEs16(vuu9, vuu110, fg) new_esEs15(Float(vuu300, vuu301), Float(vuu3100, vuu3101)) -> new_esEs8(new_sr(vuu300, vuu3101), new_sr(vuu301, vuu3100)) new_esEs19(Right(vuu300), Right(vuu3100), beh, app(app(app(ty_@3, bge), bgf), bgg)) -> new_esEs10(vuu300, vuu3100, bge, bgf, bgg) The set Q consists of the following terms: new_esEs22(Just(x0), Just(x1), ty_Int) new_primPlusNat1(Succ(x0), x1) new_esEs12(x0, x1, ty_Float) new_esEs27(x0, x1, ty_Double) new_esEs25(x0, x1, ty_Double) new_esEs12(x0, x1, ty_Double) new_esEs13(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Ordering) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs28(x0, x1, ty_Ordering) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_primPlusNat0(Zero, Succ(x0)) new_esEs5(x0, x1, ty_Char) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs28(x0, x1, app(ty_Ratio, x2)) new_esEs28(x0, x1, app(ty_[], x2)) new_esEs19(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs12(x0, x1, ty_Ordering) new_esEs11(x0, x1, app(ty_Maybe, x2)) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_Int) new_esEs19(Left(x0), Left(x1), ty_@0, x2) new_esEs23(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_esEs6(Integer(x0), Integer(x1)) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs27(x0, x1, ty_Float) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs28(x0, x1, ty_Float) new_groupByZs1(x0, [], x1) new_esEs13(x0, x1, ty_Ordering) new_esEs5(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Int) new_primEqNat0(Zero, Succ(x0)) new_esEs13(x0, x1, ty_Float) new_groupByZs1(x0, :(x1, x2), x3) new_primEqInt(Pos(Zero), Pos(Zero)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(x0, x1, app(ty_[], x2)) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs28(x0, x1, ty_Double) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_span2Ys1(x0, :(x1, x2), x3) new_esEs28(x0, x1, ty_Char) new_esEs26(x0, x1, ty_Double) new_primEqNat0(Succ(x0), Zero) new_esEs19(Right(x0), Right(x1), x2, ty_Integer) new_esEs26(x0, x1, ty_Ordering) new_esEs28(x0, x1, ty_Int) new_esEs22(Nothing, Nothing, x0) new_esEs19(Left(x0), Right(x1), x2, x3) new_esEs19(Right(x0), Left(x1), x2, x3) new_esEs26(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Char) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs16(:(x0, x1), [], x2) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs12(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs11(x0, x1, ty_Integer) new_span2Zs00(x0, x1, x2, x3, x4, x5) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, ty_@0) new_groupByZs10(x0, x1, x2, False, x3) new_esEs11(x0, x1, ty_Float) new_primPlusNat0(Zero, Zero) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs19(Left(x0), Left(x1), ty_Int, x2) new_esEs12(x0, x1, ty_Char) new_groupByZs10(x0, x1, x2, True, x3) new_esEs4(x0, x1, ty_Float) new_esEs13(x0, x1, app(ty_[], x2)) new_esEs11(x0, x1, ty_Ordering) new_esEs21(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs4(x0, x1, ty_Bool) new_esEs19(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs17(LT, EQ) new_esEs17(EQ, LT) new_span2Ys01(x0, x1, x2, x3, x4, x5) new_esEs4(x0, x1, ty_@0) new_esEs5(x0, x1, ty_Ordering) new_esEs9(False, False) new_esEs27(x0, x1, ty_Integer) new_esEs16([], [], x0) new_esEs22(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Int) new_esEs17(GT, GT) new_esEs26(x0, x1, ty_Bool) new_esEs12(x0, x1, ty_Int) new_span2Zs01(x0, x1, x2, True, x3) new_esEs22(Just(x0), Just(x1), ty_Float) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs17(EQ, GT) new_esEs17(GT, EQ) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs19(Left(x0), Left(x1), ty_Double, x2) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs19(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs22(Just(x0), Just(x1), ty_@0) new_esEs17(EQ, EQ) new_esEs22(Just(x0), Just(x1), ty_Double) new_esEs19(Left(x0), Left(x1), ty_Bool, x2) new_esEs22(Just(x0), Just(x1), ty_Char) new_esEs28(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, ty_Integer) new_span2Ys00(x0, x1, x2, True, x3) new_esEs12(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, ty_Double) new_esEs19(Left(x0), Left(x1), ty_Char, x2) new_esEs27(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Char) new_sr(Neg(x0), Neg(x1)) new_esEs22(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs11(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs25(x0, x1, ty_Bool) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, ty_Integer) new_esEs17(LT, GT) new_esEs17(GT, LT) new_esEs12(x0, x1, ty_@0) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs27(x0, x1, ty_@0) new_esEs14(@0, @0) new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primMulNat0(Succ(x0), Zero) new_esEs12(x0, x1, ty_Bool) new_esEs13(x0, x1, ty_Integer) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_primMulNat0(Zero, Succ(x0)) new_esEs24(x0, x1, ty_Integer) new_esEs28(x0, x1, ty_Bool) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs27(x0, x1, ty_Bool) new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_@0) new_span2Zs1(x0, :(x1, x2), x3) new_esEs8(x0, x1) new_esEs19(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(Just(x0), Just(x1), ty_Integer) new_span2Zs1(x0, [], x1) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_esEs20(Char(x0), Char(x1)) new_esEs19(Right(x0), Right(x1), x2, ty_Double) new_esEs28(x0, x1, ty_Integer) new_esEs15(Float(x0, x1), Float(x2, x3)) new_esEs19(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_span2Ys1(x0, [], x1) new_esEs11(x0, x1, ty_@0) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Integer) new_esEs19(Left(x0), Left(x1), ty_Float, x2) new_esEs22(Just(x0), Just(x1), ty_Bool) new_esEs4(x0, x1, ty_Integer) new_primPlusNat1(Zero, x0) new_esEs19(Right(x0), Right(x1), x2, ty_Int) new_esEs16([], :(x0, x1), x2) new_esEs28(x0, x1, ty_@0) new_esEs16(:(x0, x1), :(x2, x3), x4) new_esEs7(Double(x0, x1), Double(x2, x3)) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(Right(x0), Right(x1), x2, ty_Float) new_esEs12(x0, x1, ty_Integer) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs9(False, True) new_esEs9(True, False) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs5(x0, x1, ty_Bool) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs19(Right(x0), Right(x1), x2, ty_Ordering) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_primEqNat0(Zero, Zero) new_esEs27(x0, x1, ty_Char) new_esEs4(x0, x1, ty_Ordering) new_esEs5(x0, x1, ty_@0) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs19(Left(x0), Left(x1), ty_Integer, x2) new_esEs22(Just(x0), Just(x1), app(ty_[], x2)) new_esEs19(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs17(LT, LT) new_esEs5(x0, x1, ty_Double) new_span2Ys00(x0, x1, x2, False, x3) new_esEs26(x0, x1, ty_@0) new_esEs28(x0, x1, app(app(ty_Either, x2), x3)) new_esEs11(x0, x1, app(ty_[], x2)) new_esEs11(x0, x1, ty_Int) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_asAs(False, x0) new_asAs(True, x0) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs19(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs22(Nothing, Just(x0), x1) new_esEs19(Left(x0), Left(x1), ty_Ordering, x2) new_esEs19(Right(x0), Right(x1), x2, ty_Char) new_esEs26(x0, x1, ty_Float) new_esEs28(x0, x1, app(app(ty_@2, x2), x3)) new_esEs13(x0, x1, ty_@0) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_sr(Pos(x0), Pos(x1)) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Just(x0), Nothing, x1) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(x0, x1, app(ty_Ratio, x2)) new_esEs22(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs13(x0, x1, ty_Double) new_esEs11(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs25(x0, x1, ty_Integer) new_esEs11(x0, x1, ty_Double) new_esEs22(Just(x0), Just(x1), ty_Ordering) new_esEs25(x0, x1, app(ty_[], x2)) new_span2Zs01(x0, x1, x2, False, x3) new_esEs13(x0, x1, ty_Bool) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs11(x0, x1, ty_Char) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs9(True, True) new_esEs11(x0, x1, app(ty_Ratio, x2)) new_esEs12(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(Right(x0), Right(x1), x2, ty_Bool) new_esEs11(x0, x1, ty_Bool) new_esEs13(x0, x1, ty_Char) new_esEs5(x0, x1, ty_Float) new_esEs27(x0, x1, ty_Int) new_esEs22(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs19(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(:(x_1, x_2)) = 1 + x_2 POL(:%(x_1, x_2)) = 0 POL(@0) = 0 POL(@2(x_1, x_2)) = 0 POL(@3(x_1, x_2, x_3)) = 0 POL(Char(x_1)) = 0 POL(Double(x_1, x_2)) = 0 POL(EQ) = 0 POL(False) = 1 POL(Float(x_1, x_2)) = 0 POL(GT) = 0 POL(Integer(x_1)) = 0 POL(Just(x_1)) = 0 POL(LT) = 0 POL(Left(x_1)) = 0 POL(Neg(x_1)) = 0 POL(Nothing) = 0 POL(Pos(x_1)) = 1 + x_1 POL(Right(x_1)) = 0 POL(Succ(x_1)) = 1 + x_1 POL(True) = 0 POL(Zero) = 1 POL([]) = 0 POL(app(x_1, x_2)) = x_1 POL(new_asAs(x_1, x_2)) = x_1 + x_2 POL(new_esEs10(x_1, x_2, x_3, x_4, x_5)) = 0 POL(new_esEs11(x_1, x_2, x_3)) = 1 POL(new_esEs12(x_1, x_2, x_3)) = 0 POL(new_esEs13(x_1, x_2, x_3)) = 1 + x_1 + x_2 POL(new_esEs14(x_1, x_2)) = 0 POL(new_esEs15(x_1, x_2)) = 1 POL(new_esEs16(x_1, x_2, x_3)) = 0 POL(new_esEs17(x_1, x_2)) = 1 POL(new_esEs18(x_1, x_2, x_3)) = 0 POL(new_esEs19(x_1, x_2, x_3, x_4)) = 0 POL(new_esEs20(x_1, x_2)) = 0 POL(new_esEs21(x_1, x_2, x_3, x_4)) = 1 POL(new_esEs22(x_1, x_2, x_3)) = 1 POL(new_esEs23(x_1, x_2, x_3)) = 0 POL(new_esEs24(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs25(x_1, x_2, x_3)) = 1 + x_3 POL(new_esEs26(x_1, x_2, x_3)) = 1 + x_1 + x_2 POL(new_esEs27(x_1, x_2, x_3)) = 1 + x_1 + x_2 POL(new_esEs28(x_1, x_2, x_3)) = 1 POL(new_esEs4(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs5(x_1, x_2, x_3)) = 1 + x_3 POL(new_esEs6(x_1, x_2)) = 0 POL(new_esEs7(x_1, x_2)) = 0 POL(new_esEs8(x_1, x_2)) = 0 POL(new_esEs9(x_1, x_2)) = 1 POL(new_groupByZs1(x_1, x_2, x_3)) = x_2 POL(new_groupByZs10(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_primEqInt(x_1, x_2)) = 0 POL(new_primEqNat0(x_1, x_2)) = 0 POL(new_primMulNat0(x_1, x_2)) = x_2 POL(new_primPlusNat0(x_1, x_2)) = x_1 + x_2 POL(new_primPlusNat1(x_1, x_2)) = 0 POL(new_span2Ys00(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_span2Ys01(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_4 POL(new_span2Ys1(x_1, x_2, x_3)) = x_2 POL(new_span2Zs00(x_1, x_2, x_3, x_4, x_5, x_6)) = x_5 POL(new_span2Zs01(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_span2Zs1(x_1, x_2, x_3)) = x_2 POL(new_sr(x_1, x_2)) = x_1 POL(ty_@0) = 0 POL(ty_@2) = 0 POL(ty_@3) = 1 POL(ty_Bool) = 0 POL(ty_Char) = 1 POL(ty_Double) = 0 POL(ty_Either) = 0 POL(ty_Float) = 0 POL(ty_Int) = 0 POL(ty_Integer) = 1 POL(ty_Maybe) = 0 POL(ty_Ordering) = 0 POL(ty_Ratio) = 0 POL(ty_[]) = 0 From the DPs we obtained the following set of size-change graphs: *new_groupBy(:(vuu30, vuu31), ba) -> new_groupBy(new_groupByZs1(vuu30, vuu31, ba), ba) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 > 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_span2Zs1(vuu18, [], bdc) -> [] new_span2Zs1(vuu18, :(vuu200, vuu201), bdc) -> new_span2Zs01(vuu18, vuu200, vuu201, new_esEs5(vuu18, vuu200, bdc), bdc) new_span2Zs01(vuu42, vuu43, vuu44, True, fd) -> new_span2Zs00(vuu42, vuu43, vuu44, new_span2Ys1(vuu42, vuu44, fd), new_span2Zs1(vuu42, vuu44, fd), fd) new_span2Zs01(vuu42, vuu43, vuu44, False, fd) -> :(vuu43, vuu44) new_span2Zs00(vuu42, vuu43, vuu44, vuu49, vuu48, fd) -> vuu48 new_span2Ys1(vuu9, [], ff) -> [] new_span2Ys1(vuu9, :(vuu110, vuu111), ff) -> new_span2Ys00(vuu9, vuu110, vuu111, new_esEs4(vuu9, vuu110, ff), ff) new_span2Ys01(vuu33, vuu34, vuu35, vuu47, vuu46, bbg) -> :(vuu34, vuu47) new_span2Ys00(vuu33, vuu34, vuu35, True, bbg) -> new_span2Ys01(vuu33, vuu34, vuu35, new_span2Ys1(vuu33, vuu35, bbg), new_span2Zs1(vuu33, vuu35, bbg), bbg) new_span2Ys00(vuu33, vuu34, vuu35, False, bbg) -> [] new_groupByZs10(vuu18, vuu19, vuu20, True, bdc) -> new_span2Zs1(vuu18, vuu20, bdc) new_groupByZs10(vuu18, vuu19, vuu20, False, bdc) -> :(vuu19, vuu20) new_groupByZs1(vuu30, [], ba) -> [] new_groupByZs1(vuu30, :(vuu310, vuu311), ba) -> new_groupByZs10(vuu30, vuu310, vuu311, new_esEs28(vuu30, vuu310, ba), ba) ---------------------------------------- (16) YES ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vuu30000), Succ(vuu310100)) -> new_primMulNat(vuu30000, Succ(vuu310100)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primMulNat(Succ(vuu30000), Succ(vuu310100)) -> new_primMulNat(vuu30000, Succ(vuu310100)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuu5000), Succ(vuu3101000)) -> new_primPlusNat(vuu5000, vuu3101000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat(Succ(vuu5000), Succ(vuu3101000)) -> new_primPlusNat(vuu5000, vuu3101000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(vuu3000), Succ(vuu31000)) -> new_primEqNat(vuu3000, vuu31000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primEqNat(Succ(vuu3000), Succ(vuu31000)) -> new_primEqNat(vuu3000, vuu31000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (25) YES ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_span2Ys0(vuu33, vuu34, vuu35, True, ba) -> new_span2Zs(vuu33, vuu35, ba) new_span2Ys(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys0(vuu9, vuu110, vuu111, new_esEs4(vuu9, vuu110, bb), bb) new_span2Zs0(vuu42, vuu43, vuu44, True, bd) -> new_span2Ys(vuu42, vuu44, bd) new_span2Zs(vuu18, :(vuu200, vuu201), bc) -> new_span2Zs0(vuu18, vuu200, vuu201, new_esEs5(vuu18, vuu200, bc), bc) new_span2Ys0(vuu33, vuu34, vuu35, True, ba) -> new_span2Ys(vuu33, vuu35, ba) new_span2Zs0(vuu42, vuu43, vuu44, True, bd) -> new_span2Zs(vuu42, vuu44, bd) The TRS R consists of the following rules: new_esEs12(vuu301, vuu3101, app(ty_Maybe, ed)) -> new_esEs22(vuu301, vuu3101, ed) new_esEs11(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs4(vuu9, vuu110, ty_Ordering) -> new_esEs17(vuu9, vuu110) new_esEs7(Double(vuu300, vuu301), Double(vuu3100, vuu3101)) -> new_esEs8(new_sr(vuu300, vuu3101), new_sr(vuu301, vuu3100)) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs5(vuu18, vuu200, ty_Bool) -> new_esEs9(vuu18, vuu200) new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(Just(vuu300), Just(vuu3100), ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), app(app(ty_@2, bed), bee), bdd) -> new_esEs21(vuu300, vuu3100, bed, bee) new_esEs12(vuu301, vuu3101, app(ty_[], dc)) -> new_esEs16(vuu301, vuu3101, dc) new_esEs22(Just(vuu300), Just(vuu3100), app(app(ty_Either, gf), gg)) -> new_esEs19(vuu300, vuu3100, gf, gg) new_esEs19(Left(vuu300), Left(vuu3100), app(app(ty_Either, beb), bec), bdd) -> new_esEs19(vuu300, vuu3100, beb, bec) new_esEs11(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs27(vuu300, vuu3100, app(ty_[], bhe)) -> new_esEs16(vuu300, vuu3100, bhe) new_esEs26(vuu301, vuu3101, ty_Bool) -> new_esEs9(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Float, bdd) -> new_esEs15(vuu300, vuu3100) new_esEs22(Just(vuu300), Just(vuu3100), ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs20(Char(vuu300), Char(vuu3100)) -> new_primEqNat0(vuu300, vuu3100) new_esEs9(False, False) -> True new_esEs27(vuu300, vuu3100, app(ty_Maybe, caf)) -> new_esEs22(vuu300, vuu3100, caf) new_primMulNat0(Succ(vuu30000), Succ(vuu310100)) -> new_primPlusNat1(new_primMulNat0(vuu30000, Succ(vuu310100)), vuu310100) new_esEs11(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Char) -> new_esEs20(vuu18, vuu200) new_asAs(True, vuu27) -> vuu27 new_esEs22(Just(vuu300), Just(vuu3100), app(ty_[], ga)) -> new_esEs16(vuu300, vuu3100, ga) new_esEs26(vuu301, vuu3101, app(app(ty_@2, bbg), bbh)) -> new_esEs21(vuu301, vuu3101, bbg, bbh) new_esEs22(Just(vuu300), Just(vuu3100), app(app(ty_@2, gh), ha)) -> new_esEs21(vuu300, vuu3100, gh, ha) new_primEqInt(Pos(Succ(vuu3000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu31000))) -> False new_esEs5(vuu18, vuu200, app(app(ty_@2, bda), bdb)) -> new_esEs21(vuu18, vuu200, bda, bdb) new_esEs17(LT, LT) -> True new_esEs6(Integer(vuu300), Integer(vuu3100)) -> new_primEqInt(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(ty_Maybe, bag)) -> new_esEs22(vuu300, vuu3100, bag) new_esEs19(Left(vuu300), Left(vuu3100), app(app(app(ty_@3, bdf), bdg), bdh), bdd) -> new_esEs10(vuu300, vuu3100, bdf, bdg, bdh) new_esEs26(vuu301, vuu3101, ty_Char) -> new_esEs20(vuu301, vuu3101) new_esEs27(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Double) -> new_esEs7(vuu18, vuu200) new_primEqNat0(Succ(vuu3000), Succ(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs13(vuu302, vuu3102, ty_Integer) -> new_esEs6(vuu302, vuu3102) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, ty_Double) -> new_esEs7(vuu301, vuu3101) new_esEs12(vuu301, vuu3101, app(app(ty_@2, eb), ec)) -> new_esEs21(vuu301, vuu3101, eb, ec) new_esEs4(vuu9, vuu110, ty_Float) -> new_esEs15(vuu9, vuu110) new_esEs25(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs4(vuu9, vuu110, app(app(app(ty_@3, bgc), bgd), bge)) -> new_esEs10(vuu9, vuu110, bgc, bgd, bge) new_esEs25(vuu300, vuu3100, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs10(vuu300, vuu3100, hg, hh, baa) new_esEs24(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs13(vuu302, vuu3102, ty_@0) -> new_esEs14(vuu302, vuu3102) new_esEs13(vuu302, vuu3102, ty_Ordering) -> new_esEs17(vuu302, vuu3102) new_esEs4(vuu9, vuu110, app(ty_Maybe, bhc)) -> new_esEs22(vuu9, vuu110, bhc) new_esEs9(True, True) -> True new_esEs11(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs16(:(vuu300, vuu301), :(vuu3100, vuu3101), bhd) -> new_asAs(new_esEs27(vuu300, vuu3100, bhd), new_esEs16(vuu301, vuu3101, bhd)) new_primMulNat0(Zero, Zero) -> Zero new_esEs11(vuu300, vuu3100, app(app(ty_@2, cg), da)) -> new_esEs21(vuu300, vuu3100, cg, da) new_esEs22(Nothing, Just(vuu3100), fh) -> False new_esEs22(Just(vuu300), Nothing, fh) -> False new_esEs27(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs22(Nothing, Nothing, fh) -> True new_esEs21(@2(vuu300, vuu301), @2(vuu3100, vuu3101), hd, he) -> new_asAs(new_esEs25(vuu300, vuu3100, hd), new_esEs26(vuu301, vuu3101, he)) new_esEs12(vuu301, vuu3101, ty_Float) -> new_esEs15(vuu301, vuu3101) new_esEs22(Just(vuu300), Just(vuu3100), ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, app(ty_Ratio, cd)) -> new_esEs18(vuu300, vuu3100, cd) new_esEs12(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs25(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_primEqNat0(Succ(vuu3000), Zero) -> False new_primEqNat0(Zero, Succ(vuu31000)) -> False new_esEs27(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs14(@0, @0) -> True new_esEs27(vuu300, vuu3100, app(ty_Ratio, caa)) -> new_esEs18(vuu300, vuu3100, caa) new_esEs27(vuu300, vuu3100, app(app(app(ty_@3, bhf), bhg), bhh)) -> new_esEs10(vuu300, vuu3100, bhf, bhg, bhh) new_esEs13(vuu302, vuu3102, ty_Float) -> new_esEs15(vuu302, vuu3102) new_esEs27(vuu300, vuu3100, app(app(ty_@2, cad), cae)) -> new_esEs21(vuu300, vuu3100, cad, cae) new_esEs19(Left(vuu300), Left(vuu3100), ty_@0, bdd) -> new_esEs14(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, app(app(ty_Either, dh), ea)) -> new_esEs19(vuu301, vuu3101, dh, ea) new_esEs26(vuu301, vuu3101, app(ty_Maybe, bca)) -> new_esEs22(vuu301, vuu3101, bca) new_esEs22(Just(vuu300), Just(vuu3100), app(ty_Maybe, hb)) -> new_esEs22(vuu300, vuu3100, hb) new_esEs17(EQ, GT) -> False new_esEs17(GT, EQ) -> False new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Int) -> new_esEs8(vuu18, vuu200) new_esEs4(vuu9, vuu110, app(ty_Ratio, bgf)) -> new_esEs18(vuu9, vuu110, bgf) new_esEs22(Just(vuu300), Just(vuu3100), ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, ty_Char) -> new_esEs20(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, ty_Ordering) -> new_esEs17(vuu301, vuu3101) new_esEs17(GT, GT) -> True new_primEqInt(Neg(Succ(vuu3000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu31000))) -> False new_esEs26(vuu301, vuu3101, app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs10(vuu301, vuu3101, bba, bbb, bbc) new_esEs26(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_primEqInt(Pos(Succ(vuu3000)), Pos(Succ(vuu31000))) -> new_primEqNat0(vuu3000, vuu31000) new_esEs11(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_Float) -> new_esEs15(vuu18, vuu200) new_esEs22(Just(vuu300), Just(vuu3100), ty_Integer) -> new_esEs6(vuu300, vuu3100) new_sr(Pos(vuu3000), Neg(vuu31010)) -> Neg(new_primMulNat0(vuu3000, vuu31010)) new_sr(Neg(vuu3000), Pos(vuu31010)) -> Neg(new_primMulNat0(vuu3000, vuu31010)) new_esEs5(vuu18, vuu200, app(app(ty_Either, bcg), bch)) -> new_esEs19(vuu18, vuu200, bcg, bch) new_esEs22(Just(vuu300), Just(vuu3100), ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs26(vuu301, vuu3101, ty_@0) -> new_esEs14(vuu301, vuu3101) new_primEqInt(Pos(Succ(vuu3000)), Neg(vuu3100)) -> False new_primEqInt(Neg(Succ(vuu3000)), Pos(vuu3100)) -> False new_esEs4(vuu9, vuu110, ty_Double) -> new_esEs7(vuu9, vuu110) new_esEs4(vuu9, vuu110, app(app(ty_@2, bha), bhb)) -> new_esEs21(vuu9, vuu110, bha, bhb) new_esEs19(Left(vuu300), Left(vuu3100), ty_Ordering, bdd) -> new_esEs17(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(ty_[], hf)) -> new_esEs16(vuu300, vuu3100, hf) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(ty_[], beh)) -> new_esEs16(vuu300, vuu3100, beh) new_esEs27(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), ty_Integer, bdd) -> new_esEs6(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs8(vuu30, vuu310) -> new_primEqInt(vuu30, vuu310) new_esEs22(Just(vuu300), Just(vuu3100), app(ty_Ratio, ge)) -> new_esEs18(vuu300, vuu3100, ge) new_esEs27(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(app(ty_Either, bfe), bff)) -> new_esEs19(vuu300, vuu3100, bfe, bff) new_esEs12(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_esEs18(:%(vuu300, vuu301), :%(vuu3100, vuu3101), hc) -> new_asAs(new_esEs23(vuu300, vuu3100, hc), new_esEs24(vuu301, vuu3101, hc)) new_esEs13(vuu302, vuu3102, ty_Double) -> new_esEs7(vuu302, vuu3102) new_esEs23(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_@0) -> new_esEs14(vuu300, vuu3100) new_esEs27(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_Maybe, bef), bdd) -> new_esEs22(vuu300, vuu3100, bef) new_sr(Neg(vuu3000), Neg(vuu31010)) -> Pos(new_primMulNat0(vuu3000, vuu31010)) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_[], bde), bdd) -> new_esEs16(vuu300, vuu3100, bde) new_esEs4(vuu9, vuu110, ty_Int) -> new_esEs8(vuu9, vuu110) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Bool) -> new_esEs9(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, app(ty_[], ee)) -> new_esEs16(vuu302, vuu3102, ee) new_esEs4(vuu9, vuu110, ty_Bool) -> new_esEs9(vuu9, vuu110) new_esEs13(vuu302, vuu3102, app(ty_Maybe, fg)) -> new_esEs22(vuu302, vuu3102, fg) new_esEs22(Just(vuu300), Just(vuu3100), app(app(app(ty_@3, gb), gc), gd)) -> new_esEs10(vuu300, vuu3100, gb, gc, gd) new_esEs25(vuu300, vuu3100, ty_@0) -> new_esEs14(vuu300, vuu3100) new_primEqInt(Pos(Zero), Neg(Succ(vuu31000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu31000))) -> False new_primPlusNat0(Succ(vuu5000), Succ(vuu3101000)) -> Succ(Succ(new_primPlusNat0(vuu5000, vuu3101000))) new_esEs12(vuu301, vuu3101, app(ty_Ratio, dg)) -> new_esEs18(vuu301, vuu3101, dg) new_esEs13(vuu302, vuu3102, ty_Int) -> new_esEs8(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, app(ty_[], bah)) -> new_esEs16(vuu301, vuu3101, bah) new_esEs17(EQ, EQ) -> True new_esEs4(vuu9, vuu110, app(app(ty_Either, bgg), bgh)) -> new_esEs19(vuu9, vuu110, bgg, bgh) new_primEqInt(Neg(Succ(vuu3000)), Neg(Succ(vuu31000))) -> new_primEqNat0(vuu3000, vuu31000) new_esEs17(LT, EQ) -> False new_esEs17(EQ, LT) -> False new_esEs19(Left(vuu300), Left(vuu3100), ty_Char, bdd) -> new_esEs20(vuu300, vuu3100) new_esEs13(vuu302, vuu3102, app(app(ty_Either, fb), fc)) -> new_esEs19(vuu302, vuu3102, fb, fc) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(app(ty_@2, bfg), bfh)) -> new_esEs21(vuu300, vuu3100, bfg, bfh) new_esEs12(vuu301, vuu3101, ty_Char) -> new_esEs20(vuu301, vuu3101) new_esEs25(vuu300, vuu3100, app(app(ty_Either, bac), bad)) -> new_esEs19(vuu300, vuu3100, bac, bad) new_esEs11(vuu300, vuu3100, app(app(ty_Either, ce), cf)) -> new_esEs19(vuu300, vuu3100, ce, cf) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, app(ty_Maybe, db)) -> new_esEs22(vuu300, vuu3100, db) new_primMulNat0(Succ(vuu30000), Zero) -> Zero new_primMulNat0(Zero, Succ(vuu310100)) -> Zero new_sr(Pos(vuu3000), Pos(vuu31010)) -> Pos(new_primMulNat0(vuu3000, vuu31010)) new_esEs19(Left(vuu300), Left(vuu3100), ty_Bool, bdd) -> new_esEs9(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(ty_Maybe, bga)) -> new_esEs22(vuu300, vuu3100, bga) new_esEs11(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs5(vuu18, vuu200, app(ty_Ratio, bcf)) -> new_esEs18(vuu18, vuu200, bcf) new_primPlusNat1(Succ(vuu500), vuu310100) -> Succ(Succ(new_primPlusNat0(vuu500, vuu310100))) new_esEs27(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs17(LT, GT) -> False new_esEs17(GT, LT) -> False new_esEs22(Just(vuu300), Just(vuu3100), ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs24(vuu301, vuu3101, ty_Integer) -> new_esEs6(vuu301, vuu3101) new_esEs12(vuu301, vuu3101, ty_Ordering) -> new_esEs17(vuu301, vuu3101) new_primPlusNat0(Succ(vuu5000), Zero) -> Succ(vuu5000) new_primPlusNat0(Zero, Succ(vuu3101000)) -> Succ(vuu3101000) new_esEs11(vuu300, vuu3100, app(app(app(ty_@3, ca), cb), cc)) -> new_esEs10(vuu300, vuu3100, ca, cb, cc) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(vuu301, vuu3101, app(ty_Ratio, bbd)) -> new_esEs18(vuu301, vuu3101, bbd) new_esEs13(vuu302, vuu3102, ty_Bool) -> new_esEs9(vuu302, vuu3102) new_esEs26(vuu301, vuu3101, app(app(ty_Either, bbe), bbf)) -> new_esEs19(vuu301, vuu3101, bbe, bbf) new_primPlusNat1(Zero, vuu310100) -> Succ(vuu310100) new_esEs26(vuu301, vuu3101, ty_Double) -> new_esEs7(vuu301, vuu3101) new_esEs5(vuu18, vuu200, ty_Integer) -> new_esEs6(vuu18, vuu200) new_esEs10(@3(vuu300, vuu301, vuu302), @3(vuu3100, vuu3101, vuu3102), be, bf, bg) -> new_asAs(new_esEs11(vuu300, vuu3100, be), new_asAs(new_esEs12(vuu301, vuu3101, bf), new_esEs13(vuu302, vuu3102, bg))) new_esEs12(vuu301, vuu3101, app(app(app(ty_@3, dd), de), df)) -> new_esEs10(vuu301, vuu3101, dd, de, df) new_esEs5(vuu18, vuu200, app(ty_Maybe, bdc)) -> new_esEs22(vuu18, vuu200, bdc) new_esEs12(vuu301, vuu3101, ty_Bool) -> new_esEs9(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Double, bdd) -> new_esEs7(vuu300, vuu3100) new_esEs11(vuu300, vuu3100, ty_Ordering) -> new_esEs17(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs4(vuu9, vuu110, ty_Char) -> new_esEs20(vuu9, vuu110) new_esEs26(vuu301, vuu3101, ty_Int) -> new_esEs8(vuu301, vuu3101) new_esEs5(vuu18, vuu200, app(ty_[], bcb)) -> new_esEs16(vuu18, vuu200, bcb) new_esEs27(vuu300, vuu3100, app(app(ty_Either, cab), cac)) -> new_esEs19(vuu300, vuu3100, cab, cac) new_esEs13(vuu302, vuu3102, app(app(ty_@2, fd), ff)) -> new_esEs21(vuu302, vuu3102, fd, ff) new_esEs16(:(vuu300, vuu301), [], bhd) -> False new_esEs16([], :(vuu3100, vuu3101), bhd) -> False new_esEs13(vuu302, vuu3102, app(app(app(ty_@3, ef), eg), eh)) -> new_esEs10(vuu302, vuu3102, ef, eg, eh) new_esEs4(vuu9, vuu110, ty_@0) -> new_esEs14(vuu9, vuu110) new_esEs27(vuu300, vuu3100, ty_Float) -> new_esEs15(vuu300, vuu3100) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(vuu9, vuu110, ty_Integer) -> new_esEs6(vuu9, vuu110) new_esEs19(Left(vuu300), Left(vuu3100), app(ty_Ratio, bea), bdd) -> new_esEs18(vuu300, vuu3100, bea) new_primEqNat0(Zero, Zero) -> True new_esEs16([], [], bhd) -> True new_esEs25(vuu300, vuu3100, ty_Int) -> new_esEs8(vuu300, vuu3100) new_esEs5(vuu18, vuu200, ty_@0) -> new_esEs14(vuu18, vuu200) new_esEs9(False, True) -> False new_esEs9(True, False) -> False new_esEs22(Just(vuu300), Just(vuu3100), ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, ty_Float) -> new_esEs15(vuu300, vuu3100) new_esEs12(vuu301, vuu3101, ty_@0) -> new_esEs14(vuu301, vuu3101) new_esEs19(Left(vuu300), Left(vuu3100), ty_Int, bdd) -> new_esEs8(vuu300, vuu3100) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(ty_Ratio, bfd)) -> new_esEs18(vuu300, vuu3100, bfd) new_esEs26(vuu301, vuu3101, ty_Float) -> new_esEs15(vuu301, vuu3101) new_esEs5(vuu18, vuu200, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs10(vuu18, vuu200, bcc, bcd, bce) new_esEs13(vuu302, vuu3102, app(ty_Ratio, fa)) -> new_esEs18(vuu302, vuu3102, fa) new_asAs(False, vuu27) -> False new_esEs19(Left(vuu300), Right(vuu3100), beg, bdd) -> False new_esEs19(Right(vuu300), Left(vuu3100), beg, bdd) -> False new_esEs23(vuu300, vuu3100, ty_Integer) -> new_esEs6(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(ty_Ratio, bab)) -> new_esEs18(vuu300, vuu3100, bab) new_esEs5(vuu18, vuu200, ty_Ordering) -> new_esEs17(vuu18, vuu200) new_esEs25(vuu300, vuu3100, ty_Double) -> new_esEs7(vuu300, vuu3100) new_esEs25(vuu300, vuu3100, app(app(ty_@2, bae), baf)) -> new_esEs21(vuu300, vuu3100, bae, baf) new_esEs11(vuu300, vuu3100, app(ty_[], bh)) -> new_esEs16(vuu300, vuu3100, bh) new_esEs4(vuu9, vuu110, app(ty_[], bgb)) -> new_esEs16(vuu9, vuu110, bgb) new_esEs15(Float(vuu300, vuu301), Float(vuu3100, vuu3101)) -> new_esEs8(new_sr(vuu300, vuu3101), new_sr(vuu301, vuu3100)) new_esEs19(Right(vuu300), Right(vuu3100), beg, app(app(app(ty_@3, bfa), bfb), bfc)) -> new_esEs10(vuu300, vuu3100, bfa, bfb, bfc) The set Q consists of the following terms: new_esEs22(Just(x0), Just(x1), ty_Int) new_esEs26(x0, x1, app(ty_[], x2)) new_primPlusNat1(Succ(x0), x1) new_esEs11(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(x0, x1, ty_Float) new_esEs27(x0, x1, ty_Double) new_esEs25(x0, x1, ty_Double) new_esEs12(x0, x1, ty_Double) new_esEs13(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Float) new_esEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs16(:(x0, x1), :(x2, x3), x4) new_esEs25(x0, x1, ty_Ordering) new_esEs11(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(Right(x0), Right(x1), x2, ty_Double) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_primPlusNat0(Zero, Succ(x0)) new_esEs5(x0, x1, ty_Char) new_esEs11(x0, x1, app(ty_Ratio, x2)) new_esEs19(Right(x0), Right(x1), x2, ty_Ordering) new_esEs12(x0, x1, ty_Ordering) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_Int) new_esEs23(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_primPlusNat0(Succ(x0), Zero) new_esEs6(Integer(x0), Integer(x1)) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs27(x0, x1, ty_Float) new_esEs22(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, ty_Ordering) new_esEs5(x0, x1, ty_Int) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs25(x0, x1, ty_Int) new_primEqNat0(Zero, Succ(x0)) new_esEs13(x0, x1, ty_Float) new_primEqInt(Pos(Zero), Pos(Zero)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs25(x0, x1, app(ty_[], x2)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs19(Left(x0), Left(x1), ty_Integer, x2) new_esEs19(Left(x0), Right(x1), x2, x3) new_esEs19(Right(x0), Left(x1), x2, x3) new_esEs26(x0, x1, ty_Double) new_primEqNat0(Succ(x0), Zero) new_esEs26(x0, x1, ty_Ordering) new_esEs19(Left(x0), Left(x1), ty_Float, x2) new_esEs11(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Char) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs11(x0, x1, ty_Integer) new_esEs19(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs26(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, ty_Float) new_esEs11(x0, x1, ty_Float) new_primPlusNat0(Zero, Zero) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs12(x0, x1, ty_Char) new_esEs19(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs12(x0, x1, app(ty_Ratio, x2)) new_esEs19(Left(x0), Left(x1), ty_Ordering, x2) new_esEs4(x0, x1, ty_Float) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs11(x0, x1, ty_Ordering) new_esEs19(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs4(x0, x1, ty_Bool) new_esEs19(Right(x0), Right(x1), x2, ty_Char) new_esEs17(LT, EQ) new_esEs17(EQ, LT) new_esEs4(x0, x1, ty_@0) new_esEs5(x0, x1, ty_Ordering) new_esEs16(:(x0, x1), [], x2) new_esEs9(False, False) new_esEs27(x0, x1, ty_Integer) new_esEs19(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs19(Right(x0), Right(x1), x2, ty_Int) new_esEs4(x0, x1, ty_Int) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs17(GT, GT) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs26(x0, x1, ty_Bool) new_esEs12(x0, x1, ty_Int) new_esEs22(Just(x0), Just(x1), ty_Float) new_esEs17(EQ, GT) new_esEs17(GT, EQ) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs16([], [], x0) new_esEs22(Just(x0), Just(x1), ty_@0) new_esEs17(EQ, EQ) new_esEs22(Just(x0), Just(x1), ty_Double) new_esEs22(Just(x0), Just(x1), ty_Char) new_esEs12(x0, x1, app(app(ty_Either, x2), x3)) new_esEs12(x0, x1, app(ty_[], x2)) new_esEs5(x0, x1, ty_Integer) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, ty_Double) new_esEs27(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Char) new_sr(Neg(x0), Neg(x1)) new_esEs19(Right(x0), Right(x1), x2, ty_Bool) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs19(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs22(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs25(x0, x1, ty_Bool) new_esEs26(x0, x1, ty_Integer) new_esEs19(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs19(Right(x0), Right(x1), x2, ty_@0) new_esEs17(LT, GT) new_esEs17(GT, LT) new_esEs12(x0, x1, ty_@0) new_esEs27(x0, x1, ty_@0) new_esEs14(@0, @0) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_primMulNat0(Succ(x0), Zero) new_esEs19(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs12(x0, x1, ty_Bool) new_esEs13(x0, x1, ty_Integer) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_primMulNat0(Zero, Succ(x0)) new_esEs24(x0, x1, ty_Integer) new_esEs12(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs27(x0, x1, ty_Bool) new_esEs25(x0, x1, ty_@0) new_esEs8(x0, x1) new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Just(x0), Just(x1), ty_Integer) new_esEs19(Left(x0), Left(x1), ty_Char, x2) new_esEs20(Char(x0), Char(x1)) new_esEs15(Float(x0, x1), Float(x2, x3)) new_esEs22(Nothing, Nothing, x0) new_esEs22(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs11(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Integer) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Just(x0), Just(x1), ty_Bool) new_esEs4(x0, x1, ty_Integer) new_esEs19(Left(x0), Left(x1), ty_@0, x2) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Zero, x0) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs7(Double(x0, x1), Double(x2, x3)) new_esEs19(Right(x0), Right(x1), x2, ty_Integer) new_esEs12(x0, x1, ty_Integer) new_esEs9(False, True) new_esEs9(True, False) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs5(x0, x1, ty_Bool) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_esEs19(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs11(x0, x1, app(ty_[], x2)) new_esEs12(x0, x1, app(ty_Maybe, x2)) new_esEs21(@2(x0, x1), @2(x2, x3), x4, x5) new_primEqNat0(Zero, Zero) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs27(x0, x1, ty_Char) new_esEs4(x0, x1, ty_Ordering) new_esEs5(x0, x1, ty_@0) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs22(Nothing, Just(x0), x1) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16([], :(x0, x1), x2) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs17(LT, LT) new_esEs5(x0, x1, ty_Double) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, ty_@0) new_esEs13(x0, x1, app(ty_[], x2)) new_esEs19(Left(x0), Left(x1), ty_Int, x2) new_esEs11(x0, x1, ty_Int) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_asAs(False, x0) new_asAs(True, x0) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs19(Left(x0), Left(x1), ty_Double, x2) new_esEs22(Just(x0), Just(x1), app(ty_[], x2)) new_esEs26(x0, x1, ty_Float) new_esEs13(x0, x1, ty_@0) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_sr(Pos(x0), Pos(x1)) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs13(x0, x1, ty_Double) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Integer) new_esEs19(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs11(x0, x1, ty_Double) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(Just(x0), Just(x1), ty_Ordering) new_esEs22(Just(x0), Nothing, x1) new_esEs13(x0, x1, ty_Bool) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs11(x0, x1, ty_Char) new_esEs9(True, True) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(Left(x0), Left(x1), ty_Bool, x2) new_esEs11(x0, x1, ty_Bool) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_esEs13(x0, x1, ty_Char) new_esEs5(x0, x1, ty_Float) new_esEs27(x0, x1, ty_Int) new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_span2Zs(vuu18, :(vuu200, vuu201), bc) -> new_span2Zs0(vuu18, vuu200, vuu201, new_esEs5(vuu18, vuu200, bc), bc) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 >= 5 *new_span2Ys(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys0(vuu9, vuu110, vuu111, new_esEs4(vuu9, vuu110, bb), bb) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 >= 5 *new_span2Ys0(vuu33, vuu34, vuu35, True, ba) -> new_span2Ys(vuu33, vuu35, ba) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Ys0(vuu33, vuu34, vuu35, True, ba) -> new_span2Zs(vuu33, vuu35, ba) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Zs0(vuu42, vuu43, vuu44, True, bd) -> new_span2Ys(vuu42, vuu44, bd) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Zs0(vuu42, vuu43, vuu44, True, bd) -> new_span2Zs(vuu42, vuu44, bd) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 ---------------------------------------- (28) YES